We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We further identify that the elementary excitations are fractionalized spinons.
The ground-state phase diagram of a spin-1/2 XXZ chain with competing ferromagnetic nearest-neighbor (J_1<0) and antiferromagnetic second-neighbor (J_2>0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range -4<J_1/J_2<0 has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid st…
Neutron diffraction experiments performed on the Haldane gap material NDMAP in high magnetic fields applied at an angle to the principal anisotropy axes reveal two consecutive field-induced phase transitions. The low-field phase is the gapped Haldane state, while at high fields the system exhibits 3-dimensional long-range Neel order. In a peculiar phase found at intermediate fields only half of all the spin chains participate in the long-range ordering, while the other half remains disordered and gapped.
We study both the static and dynamic properties of gapped, one-dimensional, Heisenberg, anti-ferromagnetic, spin chains at finite temperature through an analysis of the O(3) non-linear sigma model. Exploiting the integrability of this theory, we are able to compute an exact low temperature expansion of the finite temperature correlators. We do so using a truncated `form-factor' expansion and so provide evidence that this technique can be successfully extended to finite temperature. As a direct test, we compute the static zero-field susceptibility and obtain an exact match to the susceptibility…
We use the variational matrix-product ansatz to study elementary excitations in the S=1/2 ladder with additional diagonal coupling, equivalent to a single S=1/2 chain with alternating exchange and next-nearest neighbor interaction. In absence of alternation the elementary excitation consists of two free S=1/2 particles ("spinons") which are solitons in the dimer order. When the nearest-neighbor exchange alternates, the "spinons" are confined into one S=1 excitation being a soliton in the generalized string order. Variational results are found to be in a qualitative agreement with the exact dia…
Recent experiments on the quasi-1D antiferromagnets $R_{2}BaNiO_{5}$ (R = rare earth) have shown the existence of purely 1D Haldane gap excitations propagating on the Ni chains. Below an ordering temperature, the gap excitations survive and coexist with the conventional spin waves in the ordered phase. We construct a model mixed-spin system in 2D for which the ground state can be exactly specified. Using the Matrix Product Method, we show the existence of Haldane gap excitations in the ordered phase. We consider different cases of ordering to study the effect of ordering on the degeneracy of t…
Using the density matrix renormalization group (DMRG) technique, we carry out a large scale numerical calculation for the S=2 antiferromagnetic Heisenberg chain. Performing systematic scaling analysis for both the chain length $L$ and the number of optimal states kept in the iterations $m$, the Haldane gap $Δ(2)$ is estimated accurately as $(0.0876\pm0.0013)J$. Our systematic analysis for the S=2 chains not only ends the controversies arising from various DMRG calculations and Monte Carlo simulations, but also sheds light on how to obtain reliable results from the DMRG calculations for other c…
The impurity-induced antiferromagnetic ordering of the doped Haldane magnet Pb(Ni{1-x}Mg{x})2V2O8 (0 < x <0.06) was studied by electron spin resonance (ESR) on ceramic samples in the frequency range 9-110 GHz. Below the Néel temperature a transformation of the ESR spectrum was found, indicating an antiferromagnetic resonance mode of spin precession. The excitation gap of the spin-wave spectrum increases with increasing Mg-concentration $x$ in the same manner as the Néel temperature, reaching its maximum value of 80 GHz at x > 0.04. At small concentrations x < 0.02 the signals of antiferromagne…
The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.
We formulate the dynamics of local order parameters by extending the recently developed adiabatic spinwave theory involving the Berry curvature, and derive a formula showing explicitly the role of the Berry phase in determining the spectral form of the low-lying collective modes. For antiferromagnetic spin chains, the Berry phase becomes a topological invariant known as the Chern number. Our theory predicts the existence of the Haldane gap for a topologically trivial ground state, and a linear dispersion of low-lying excitations for a non-trivial ground state.
We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains in the presence of a magnetic field exceeding the attendant spin gap. For temperatures much smaller than the gap, the spin chains exhibit Luttinger liquid behavior. We compute exactly both the corresponding Luttinger parameter and the Fermi velocity as a function of magnetic field. This enables the computation of a number of correlators from which we derive the spin conductance, the expected form of the dynamic structure factor relevant to inelastic neutron scattering experiments, and NMR relaxation rates. We also comm…
The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF$_{1}$-AF$_{2}$-AF$_{1}$% -F (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density matrix renormalization group method. Two plateaux of magnetization $m$ are found at $m=0$ and 1/4% . It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped state…
We construct and study a time reversal broken tight binding model on diamond lattice with complex next-nearest-neighbour hopping which can be thought of as a generalisation of two dimensional Haldane model in three dimension. The model also breaks inversion symmetry owing to sub-lattice dependent chemical potential. We calculate the spectrum of the model and find the existence of six pairs of anisotropic gapless points with linear dependence on momentum. The coordinates of the gapless points are ($2 π, π\pm k_0,0),~ (2 π, π\pm k_0,2 π)$ and their possible permutations . The condition for gaple…
The spin dynamics of the S=1 Ni-chains in mixed-spin antiferromagnets Pr_2 Ba Ni O_5 and Nd_x Y_2-x Ba Ni O_5 is described in terms of a simple Ginzburg-Landau Lagrangian coupled to the sublattice of rare-earth ions. Within this framework we obtain a theoretical explanation for the experimentally observed coexistence of Haldane gap excitations and long-range magnetic order, as well as for the increase of the Haldane gap energy below the Neel point. We also predict that the degeneracy of the Haldane triplet is lifted in the magnetically ordered phase. The theoretical results are consistent with…
The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappear…
The one-dimensional Heisenberg antiferromagnets of large-integer-$S$ spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for $S=5$ and $6$. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for $S=5$ and $6$ are …
We consider the one dimensional, periodic spin chain with $N$ sites, similar to the one studied by Haldane \cite{hal}, however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude $s$. For a chain with an even number of sites we show that actually the ground state is non degenerate and given by a superposition of the two Néel states, due to quantum spin tunnelling. With an odd number of sites, the Néel state must necessarily contain a soliton. The position of the soliton is arbitrary thu…
We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weigh…
Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications …
Non-magnetic floating phases in frustrated Haldane chains with a single-ion anisotropy
Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）
We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The…
We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Hal…
We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with onsite repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first order…
It is conjectured that the Haldane phase of the S=1 antiferromagnetic Heisenberg chain and the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain is stable against any strength of randomness, because of imposed breakdown of translational symmetry. This conjecture is confirmed by the density matrix renormalization group calculation of the string order parameter and the energy gap distribution.
We propose an exotic scenario that topological superconductivity can emerge by doping strongly interacting fermionic systems whose spin degrees of freedom form bosonic symmetry protected topological (SPT) state. Specifically, we study a 1-dimensional (1D) example where the spin degrees of freedom form a spin-1 Haldane phase. {Before doping, the charge and spin degrees of freedom are both gapped.} Upon doping, {the charge channel becomes gapless and is described by a $c=1$ compactified bosonic conformal field theory (CFT), while the spin channel remains gapped and still form a bosonic SPT state…
We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y$_2$BaNi$_{1-x}$Zn$_x$O$_5$. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility $χ(T) \sim C / (Θ+T)$ as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the …
In order to clarify a key role of orbital degree of freedom in the spin S=1 Haldane system, we investigate ground-state properties of the t2g-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multi-orbital systems, in general, there occurs a transition from an antiferromagnetic to a ferromagnetic phase. We find that the antiferromagnetic phase is described as the Haldane system with spin gap, while in the ferromagnetic phase, there exists the gapless excitation with respect to orbital degree of freedom. Possible relevance…
We study the bulk entanglement of a series of gapped ground states of spin ladders, representative of the Haldane phase. These ground states of spin $S/2$ ladders generalize the valence bond solid ground state. In the case of spin 1/2 ladders, we study a generalization of the Affleck-Kennedy-Lieb-Tasaki and Nersesyan-Tsvelik states and fully characterize the bulk entanglement Hamiltonian. In the case of general spin $S$ we argue that in the Haldane phase the bulk entanglement spectrum of a half integer ladder is either gapless or possess a degenerate ground state. For ladders with integer valu…
The NMR relaxation rates of (quasi-)one-dimensional spin gapped systems such as the $S=1/2$ spin ladder with a diagonal interaction and the Haldane-gap system are investigated at low temperatures in magnetic fields. We show that in the regime where the gap is collapsed by magnetic fields, the NMR relaxation rate diverges with decreasing temperature and its exponent shows a behavior characteristic of the model as a function of magnetic field. We discuss our results in comparison with recent experimental findings for the spin ladder system ${\rm Cu_{2}(C_{5}H_{12}N_{2})_{2}Cl_{4}}$ and for the H…
We reexamine the one-dimensional spin-1 $XXZ$ model with on-site uniaxial single-ion anisotropy as to the appearance and characterization of the symmetry-protected topological Haldane phase. By means of large-scale density-matrix renormalization group (DMRG) calculations the central charge can be determined numerically via the von Neumann entropy, from which the ground-sate phase diagram of the model can be derived with high precision. The nontrivial gapped Haldane phase shows up in between the trivial gapped even Haldane and N{é}el phases, appearing at large single-ion and spin--exchange inte…
We investigate how the antiferromagnetic Mott insulator evolves into the d-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and d-wave superconductor. This non-Fermi liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibil…
We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system CsNiCl3. Measurements over a wide range of wave-vector transfers along the chain confirm that above T_N CsNiCl3 is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length xi=4.0(2) sites at T=6.2K. This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperatur…
We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of a S=1 Haldane chain, placed in a strong external magnetic field $H$ exceeding the Haldane gap $Δ$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $ω\gtrsim Δ$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity $S^{\parallel}(q=π,ω)\propto(ω-ω_{0})^{-α'}$. We study the behavior of the high-energy edge exponent…
Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic Néel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends …
We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy based on several effective field theories, the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid, we have to take interactions among magnons into account. Though the O(3) NLSM i…
This article reviews low-temperature heat transport studies of spin-gapped quantum magnets in the last few decades. Quantum magnets with small spins and low dimensionality exhibit a variety of novel phenomena. Among them, some systems are char-acteristic of having quantum-mechanism spin gap in their magnetic excitation spectra, including spin-Peierls systems, S = 1 Haldane chains, S = 1/2 spin ladders, and spin dimmers. In some particular spin-gapped systems, the XY-type antiferromagnetic state induced by magnetic field that closes the spin gap can be described as a magnon Bose-Einstein conden…
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromag…
We obtain the phase diagram in the parameter space $(J'/J, γ)$ and an accurate estimate of the critical line separating the different phases. We show several measuments of the magnetization, dimerization, nearest neighbours correlation, and density of energy in the different zones of the phase diagram, as well as a measurement of the string order parameter proposed as the non vanishing phase order parameter characterizing Haldane phases. All these results will be compared in the limit $J'/J\gg 1$ with the behaviour of the $\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of …
We apply field theory methods to $\mbox{SU}(3)$ chains in the symmetric representation, with $p$ boxes in the Young tableau, mapping them into a flag manifold non-linear $σ$-model with a topological angle $θ=2πp/3$. Generalizing the Haldane conjecture, we argue that the models are gapped for $p=3m$ but gapless for $p=3m\pm 1$ (for integer $m$), corresponding to a massless phase of the $σ$-model at $θ=\pm 2π/3$. We confirm this with Monte Carlo calculations on the $σ$-model.
The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conc…
Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with $S=1/2$ and S=1 on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that effective magnetic moments induced around the diluted sites exhibit the antiferromagnetic long-range order in the medium of spin-singlet pairs. Their microscopic structure is examined in detail and important roles of the higher dimensionality than one on the phenomenon are discussed.
We investigate the impact of s-wave spin-singlet pairing on antiferromagnetic semimetals with Dirac points or nodal loops at the Fermi level. The electron pairing is generally shown to convert the semimetal into a tunable nodal superconductor. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the antiferromagnetic-superconducting state that set the occurrence of a large variety of electronic topological transitions. We provide a general criterion for predicting a series of transitions between nodal and fully gapped superconducting phases. Different types …
We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime ($Δ> 1$). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the $π/2$ momentum line, its overall anisotropy dependence, and its contribution to sum rules.
We present the exact solution of a one-dimensional model of a spin-gapped correlated electron system with hybridization impurities exhibiting both magnetic and mixed-valence properties. The host supports superconducting fluctuations, with a spin gap. The localized electrons create a band of antiferromagnetic spin excitations inside the gap for concentrations x of the impurities below some critical value x_c. When x = x_c the spin gap closes and a ferrimagnetic phase appears. This is the first example of an exactly solvable model with coexisting superconducting and antiferromagnetic fluctuation…
We present a novel mixed-spin cluster expansion method for a quasi-one-dimensional Haldane system with bond alternation. By mapping the s=1 antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer and the magnetically ordered phases. The mixed-spin cluster expansion proposed here allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The phase diagram is determined rather precisely by making use of an additional symmetry property in the effective…
In the O(3) sigma-model description of gapped spin systems, S=1 magnons can only decay into three lower energy magnons. We argue that the symmetry of the quantum spin Hamiltonian often allows decay into two magnons, and compute this decay rate in model systems. Two magnon decay is present in Haldane gap S=1 spin chains, even though it cannot be induced by any allowed term written in powers and gradients of the sigma-model field. We compare our results with recent measurements of Stone et al. (cond-mat/0511266) on a two-dimensional spin system.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange J. This Mott-insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation h…
A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of $N$ for attractive interactions at half-filling. The analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin $N/2$ operator which …
We consider a quasi-one-dimensional system of spin-1 Heisenberg antiferromagnetic chains in 2D and 3D hypercubic lattices with interchain coupling $J$ and uniaxial single-ion anisotropy $D$. Using large scale numerical simulations, we map out the $J-D$ phase diagram and investigate the low lying excitations of the Haldane phase in the $J\ll1$ limit. We also provide direct evidence that the Haldane phase remains a non-trivial symmetry protected topological state for small but finite $J$.
We report a single-crystal study on the magnetism of the rare-earth compound PrTiNbO$_6$ that experimentally realizes the zigzag pseudospin-$\frac{1}{2}$ quantum antiferromagnetic chain model. Random crystal electric field caused by the site mixing between non-magnetic Ti$^{4+}$ and Nb$^{5+}$, results in the non-Kramers ground state quasi-doublet of Pr$^{3+}$ with the effective pseudospin-$\frac{1}{2}$ Ising moment. Despite the antiferromagnetic intersite coupling of about 4 K, no magnetic freezing is detected down to 0.1 K, whilst the system approaches its ground state with almost zero residu…
Infinite projected entangled pair states simulations of the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and 3-sublattice 120$^\circ$ magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled $S=1$ chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.
Applying a symmetric bulk bipartition to one-dimensional Affleck-Kennedy-Lieb-Tasaki valence bond solid (VBS) states for the integer spin-S Haldane gapped phase, we can create an array of fractionalized spin-S/2 edge states with the super unit cell $l$ in the reduced bulk system, and the topological properties encoded in the VBS wave functions can be revealed. The entanglement Hamiltonian (EH) with $l=even$ corresponds to the quantum antiferromagnetic Heisenberg spin-S/2 model. For the even integer spins, the EH still describes the Haldane gapped phase. For the odd integer spins, however, the …
Motivated by the recent generalization of the Haldane conjecture to $\mathrm{SU}(3)$ chains [M. Lajkó et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a multiple of three, we develop a density matrix renormalization group algorithm based on standard Young tableaus to study the model with three boxes directly in the representations of the global $\mathrm{SU}(3)$ symmetry. We show that there is a finite gap between the singlet and the symmetric $[3\,0\,0]$ sector $Δ_{[3\,0\,0]}/J …
We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descrip…
We present a systematic perturbative approach to study excitations in the thin cylinder/torus limit of the quantum Hall states. The approach is applied to the Haldane-Rezayi and Gaffnian quantum Hall states, which are both expected to have gapless excitations in the usual two-dimensional thermodynamic limit. For the Haldane-Rezayi state, we confirm that gapless excitations are present also in the "one-dimensional" thermodynamic limit of an infinite thin cylinder, in agreement with earlier considerations based on the wave functions alone. In contrast, we identify the lowest excitations of the G…
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitr…
The ground state of the $S=1$ antiferromagnetic Heisenberg chain belongs to the Haldane phase -- a well known example of symmetry-protected topological phase. A staggered field applied to the $S=1$ antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase.…
The interplay between antiferromagnetic interaction and hole motion is capable of inducing intriguing conducting topological Haldane phases described by a finite non-local string order parameter. Here we show that these states of matter are captured by the one dimensional $t-J_z$ model which can be experimentally realized with dressed Rydberg atoms trapped onto a one dimensional optical lattice. In the sector with vanishing total magnetization exact Bethe ansatz calculations associated to bosonization technique allow to predict that both metallic and superconducting topological Haldane states …
We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Ou…
