The spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice represents one of the simplest examples in which the effets of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for $J_2/J_1 \approx 0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48 \lesssim J_2/J_1 \lesssim 0.54$) and a valence-bond solid (for $0.54 \lesssim J_2/J_1 \lesssim 0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A.W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)] reconcile the contraddicting results obtained within different approaches over the years.
We report results of an electron spin resonance (ESR) study of a spin-gap antiferromagnet (C$_4$H$_{12}$N$_2$)(Cu$_2$Cl$_6$) (nicknamed PHCC) with chlorine ions partially substituted by bromine. We found that up to 10% of nominal doping the contribution of the random defects to the absorption spectra remains at about 0.1% per copper ion, almost the same as in the pure system. Instead, a particular kind of ESR absorption corresponding to gapless S=1 triplets is observed at low temperatures in samples with high nominal bromine content x>5%. Increase of bromine concentration also leads to the sys…
One of the most promising candidate ground states for the quantum antiferromagnetic Heisenberg model on the Kagome lattice is the valence bond solid (VBS) with a 36-site unit cell. We present a theory of triplet excitation spectra about this ground state using bond operator formalism. In particular we obtain dispersions of all 18 triplet modes in the reduced Brillouin zone. In the bond operator mean-field theory, it is found that a large number of triplet modes are non-dispersive. In particular, the lowest triplet excitation is non-dispersive and degenerate with a dispersive mode at the zone c…
New data for the two-dimensional J1-J2 model shows that the critical points for singlet and triplet excitations near J2/J1=0.38 are very close together, or coincident. We propose that this is a more general result: in strongly frustrated spin systems the critical dynamics of singlet and triplet excitations are closely related. An effective field theory for such a critical point, or points, is developed, and its implications discussed. The analysis suggests the existance of gapless or almost gapless singlet excitations in the magnetically disordered phase.
We solve for the elementary excitation in infinite quasi-1D quantum lattices by extending the recently developed infinite quasi-1D entanglement perturbation theory. The wave function of an excited state is variationally determined by optimizing superposition of cluster operation, each of which is composed of simultaneous on-site operation inside a block of lattice sites, on the ground state in a form of plane wave. The excitation energy with respect to the wave number gives the spectra for an elementary excitation. Our method is artificial broadening free and is adaptive for various quasi-part…
A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM) consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately $0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-site cluster, consisting of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated…
We study the plaquette valence-bond solid phase of the spin-1/2 J_1-J_2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J_1-J_2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky an…
We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the Rényi entropy for splitting a torus into two cylinders, We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not iden…
We show that the optical responses below the Mott gap can be used to probe the spin-triplet excitations in valence bond solid (VBS) phases in Mott insulators. The optical conductivity in this regime arises due to the electronic polarization mechanism via virtual electron hopping processes. We apply this mechanism to the Hubbard model with spin-orbit couplings and/or the corresponding spin model with significant Dzyaloshinskii-Moriya (DM) interactions, and compute the optical conductivity of VBS states on both ideal and deformed Kagome lattices. In case of the deformed Kagome lattice, we study …
A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong onsite Hund's interactions develop intra-atomic tRVBs between the t$_{2g}$ orbitals. On doping, the presence of two iron atoms per unit cell allows thes…
We construct a class of projected entangled pair states (PEPS) which is exactly the resonating valence bond (RVB) wavefunctions endowed with both short range and long range valence bonds. With an energetically preferred RVB pattern, the wavefunction is simplified to live in a one parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin 1/2 J1-J2 antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with even or odd number of fluxes penetrating the cylinder …
We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phas…
We develop a quantum spin liquid theory for quantum magnets with easy-plane ferromagnetic exchange. These strongly entangled quantum states are obtained by dimer coverings of 2D lattices with triplet $S = 1, m_z = 0$ bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large $N$ limit. We also incorpo…
In a recent comments [arXiv:1909.12788 (2019)], Zhao et al. argue that the definition of dimer orders used in our paper [Phys. Rev. B 98, 241109 (2018)] may not rule out valence bond solid (VBS) orders of $J_1$-$J_2$ model on the open boundary conditions (OBC). In this reply, we show that their argument does not apply to our case.
Motivated by the observation of a gapless spin liquid state in $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, we analyze the anisotropic triangular lattice $S=1/2$ Heisenberg model with the resonating valence bond mean-field approximation. Paying attention to the small quasi-one-dimensional anisotropy of the material, we take an approach from one-dimensional (1D) chains coupled with frustrating zig-zag bonds. By calculating one-particle excitation spectra changing anisotropy parameter $J'/J$ from the decoupled 1D chains to the isotropic triangular lattice, we find almost gapless excitations in the wide ran…
This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number $n\_ω$ of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirm the parity law and the gapless character of the ribbon for even $n\_ω$.
Using a series expansion based on the flow-equation method we study the ground state energy and the elementary triplet excitations of a generalized model of crossed spin-1/2 chains starting from the limit of decoupled quadrumers. The triplet dispersion is shown to be very sensitive to the inter-quadrumer frustration, exhibiting a line of almost complete localization as well as lines of quantum phase transitions limiting the stability of the valence-bond solid phase. In the vicinity of the checkerboard-point a finite window of exchange couplings is found with a non-zero spin-gap, consistent wit…
The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{\vartriangle}$ and $J_{\triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $\mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{\triangledown}/J_{\vartriangl…
A physical model for a mixed-valence impurity in a metal must satisfy the Friedel screening theorem for both valences. Such a model is shown, following earlier work which showed low energy singularities in it, to be supersymmetric, leading to a free Majorana and a phase-shifted Majorana excitation. The theory extended approximately to a lattice of mixed-valence ions at appropriate filling gives, without fine-tuning the parameters, a protected gapless Majorana fermion band across the chemical potential, besides the mixed-valence particle and hole bands separated by gaps. In this situation the s…
In this paper we study the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting ($TS$) and spin density wave ($SDW^{z}$) instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-1/2 XY model takes place. In the case of weakly anisotropic antiferromagnetic exchange the system…
An unconventional superconducting phase is explored developing out of a non Fermi-liquid phase of the two-channel Anderson lattice model. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature peaks in the moderate intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develops in the conduction electron density of states which vanishes as…
A model for crystal field triplet ground states on rare earth or actinide ions with dipolar and quadrupolar couplings to conduction electrons is studied for the first time with renormalization group methods. The quadrupolar coupling leads to a new nontrivial, non-Fermi liquid fixed point, which survives in an intermediate valence Anderson model. The calculated magnetic susceptibility displays one parameter scaling, going as $T^{-α}$ ($α\approx 0.4$) at intermediate temperatures, reminiscent of the non-Fermi liquid alloy UCu_{5-x}Pd_x.
We propose a set of maximized string order parameters to describe the hidden topological order in the valence bond solid states of quantum integer spin-S chains. These optimized string order parameters involve spin-twist angles corresponding to $Z_{S+1}$ rotations around $z$ or $x$-axes, suggesting a hidden $Z_{S+1}\times Z_{S+1}$ symmetry. Our results also suggest that a local triplet excitation in the valence bond solid states carries a $Z_{S+1}$ topological charge measured by these maximized string order parameters.
We show that the two-channel Anderson lattice model leads to the development of an unconventional superconductivity out of a metallic non Fermi-liquid phase. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature is band filling dependent and peaks for half filling in the extrem intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develo…
Determining ground states of correlated electron systems is fundamental to understanding novel phenomena in condensed matter physics. A difficulty, however, arises in a geometrically frustrated system in which the incompatibility between the global topology of an underlying lattice and local spin interactions gives rise to macroscopically degenerate ground states, potentially prompting the emergence of quantum spin states, such as resonating valence bond (RVB) and valence bond solid (VBS). Although theoretically proposed to exist in a kagome lattice -- one of the most highly frustrated lattice…
The hardcore extended Bose Hubbard model on a bilayer square lattice with attractive (repulsive) interplane (intraplane) interactions has been investigated numerically. Focusing on the strong interplane hopping parameter regime, triplet valence bonds of dimers are stabilized to form valence bond checkerboard solid at quarter filling. Increasing the particle number we confirm, for the first time, the presence of the exotic valence bond supersolid phase, where the valence bond solid ordering and the boson superfluidity coexist. Rising further the particle number will lead to a checkerboard solid…
The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on ${\rm Cs_2 Cu Cl_4}$, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems, and remains similarly accurate in the two-dimensional model corresponding to ${\rm Cs_2 Cu …
General conditions in which disordered, spin liquid, and valence-bond ordered phases occur in quantum Ising antiferromagnets are studied using the prototype Kagome lattice spin models. A range of quantum dynamical processes in the Ising model, with and without total Ising spin conserved, are analytically shown to yield all three characteristic quantum paramagnetic phases in the Kagome system. Special emphasis is given to the XXZ model that can be sensibly compared to the Kagome lattice Heisenberg antiferromagnet. It is explicitly demonstrated that the total-spin-conserving dynamics can yield a…
We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave-functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent $1.16(4)$. This is reminiscent of the {\it classical} dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modu…
We show that when spin and orbital angular momenta are entangled by spin-orbit coupling, this transforms a topological spin-triplet superfluid/superconductor state, such as $^{3}$He-B, into a topological $s^{\pm}$ state, with non-trivial gapless edge states. Similar to $^{3}$He-B, the $s^{\pm}$ state also minimizes on-site Coulomb repulsion for weak to moderate interactions. A topological phase transition into a $d$-wave state occurs for sufficiently strong spin-orbit coupling.
The multi-layer $S={1\over 2}$ square lattice Heisenberg antiferromagnet with up to 6 layers is studied via various series expansions. For the systems with an odd number of coupled planes, the ground-state energy, staggered magnetization, and triplet excitation spectra are calculated via two different Ising expansions. The systems are found to have long range Néel order and gapless excitations for all ratios of interlayer to intralayer couplings, as for the single-layer system. For the systems with an even number of coupled planes, there is a second order transition point separating the gaples…
We present a theory for site dilution in the Valence Bond Crystal Phase of the Kagome Lattice Heisenberg Model. The presence of an empty site leads to strong singlet bond across the impurity. It also creates a free spin, which delocalizes inside the unit cell. Finite concentration of quenched impurities leads to a Valence Bond Glass phase. This phase has short-range Valence Bond order, no spin-gap, large spin susceptibilities, linear specific heat due to two-level systems, as well as singlet and triplet excitations that decompose into kink-antikink pairs delocalized over a few lattice constant…
We construct a family of rotationally invariant, local, S=1/2 Klein Hamiltonians on various lattices that exhibit ground state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models can be driven into phases modeled by well understood quantum dimer models on the corresponding lattices. Specifically, we show that the perturbation procedure is arbitrarily well controlled by a new parameter which is the extent of decoration of the reference lattice. This strategy leads to Hamiltonians that exhibit i) $Z_2$ RVB phases in two dimensions, ii) …
In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.
We study the quantum dimer model on the triangular lattice, which is expected to describe the singlet dynamics of frustrated Heisenberg models in phases where valence bond configurations dominate their physics. We find, in contrast to the square lattice, that there is a truly short ranged resonating valence bond (RVB) phase with no gapless collective excitations and with deconfined, gapped, spinons for a {\it finite} range of parameters. We also establish the presence of three crystalline phases in this system.
The two-dimensional Su-Schrieffer-Heeger model of electrons coupled to quantum phonons is investigated using Langevin dynamics within the framework of auxiliary-field quantum Monte Carlo. Based on an explicit determination of the density of zeros of the fermion determinant, it is argued that the method is efficient in the challenging adiabatic limit. Large-scale simulations at the O(4)-symmetric point establish that the ground state of the 2D SSH model undergoes a transition from a $(π,π)$ valence bond solid to an antiferromagnet with increasing phonon frequency, yet still in the adiabatic reg…
We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond bas…
We show that the mean-field resonating valence bond approximation proposed in 1987 by Baskaran, Zou, and Anderson describes gapless charge pair excitations confined to the boundaries of the spinon Brillouin zone. The existence of such pairs accounts for all the essential anomalous electronic properties of cuprates, with superconductivity arising due to the charge drag by the spinon superflow. This mechanism may be relevant to other unconventional superconductors.
In this paper we study the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-1/2 XY model takes place.
We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with Néel order, a free Dirac fermion in the π-flux phase, and the nearest-neighbor resonating-valence-bond wavefunction. For these models, we show that the entanglement entropy between cylindrical regions of length x and L - x, extending around a torus of length L, depends upon the dimensionless ratio x/L. This can be well-approximated on finite-size lattices by a function ln(sin(πx/L)), akin to the familiar chord-length depen…
We analyze the stability of the spontaneously dimerized spin-liquid phase of the frustrated Heisenberg antiferromagnet - the J1-J2 model. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region 0.38 < J2/J1 < 0.62. In addition we find a stable low-energy collective singlet mode, which is closely related to the spontaneous violation of the discrete symmetry. Both modes are gapped in the quantum disordered phase and become gapless at the transition point to the Neel ordered phase (J2/J1=0.38). The spontaneous dimerization vanishes at the tr…
We analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire comparable propensity toward the nucleation of Kekulé valence-bond solid (KVBS) and charge-density-wave ($N_b=1$) or $s$-wave pairing ($N_b=2$) or anti-ferromagnet ($N_b=3$) in honeycomb lattice, where $N_b$ counts the number of bosonic order parameter components. Besides the cubic terms present in the order parameter description of KVBS due to the breaking of a discrete $Z_3$ symmetry, quantum fluctuations generate new cubic vertice…
The frustrated Heisenberg $J_{1}-J_{2}$ model on a square lattice is numerically investigated by variational Monte Carlo simulations. We propose a antiferromagnetic fermion resonating-valence-bond (AF-fRVB) state that has ability to examine the entire phase diagram in the $J_{1}-J_{2}$ model. Two phase transition points, the second order around $J_{2}/J_{1}=0.45$ and the first order around $J_{2}/J_{1}=0.6$, can be extracted more clearly than the conventional bosonic RVB state. At the maximally frustrated point ($J_{2}/J_{1}=0.5$), the AF-fRVB state shows the variational ground-state energy in…
Using tight binding band picture for 2D graphite, and the Hubbard interaction, recently we obtained a gapless, neutral spin-1 collective mode in graphite \cite{SZS}. In this paper we present a detailed RPA analysis of the Neutron Scattering cross section for this collective mode. Near $K-$point and very close to $Γ-$point, the intensity of neutron scattering peaks vanishes as $q^3$. This is shown using a simple Dirac cone model for the graphite band structure, which captures the small$-q$ behavior of the system. As we move away from the $Γ-$ and $K-$points in the Brillouin zone of the collecti…
We study possible quantum ground states of the Sp(N) generalized Heisenberg model on a cubic lattice with nearest-neighbor and next-nearest-neighbor exchange interactions. The phase diagram is obtained in the large-N limit and fluctuation effects are considered via appropriate gauge theories. In particular, we find three U(1) spin liquid phases with different short-range magnetic correlations. These phases are characterized by deconfined gapped spinons, gapped monopoles, and gapless ``photons''. As N becomes smaller, a confinement transition from these phases to valence bond solids (VBS) may o…
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topolo…
I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) Néel with $Q=(π,π)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$, and …
We study the low-energy properties of Heisenberg antiferromagnetic spin-1/2 and spin-1 systems on various clusters made up of triangles. Some of the clusters have a geometry similar to representative pieces of the Kagome lattice, while others have the geometry of a sawtooth chain. While the ground state always has the lowest possible spin (0 or 1/2), the nature of the low-energy excitations depends on the geometry and the site spin. For the Kagome clusters with spin-1 sites, the lowest excitations are gapped, with singlet and triplet excitations having similar gaps. This is in contrast to Kago…
Fermionic valence bond approach in terms of SU(4) representation is proposed to describe the $J_{1}-J_{2}$ frustrated Heisenberg antiferromagnetic (AF) model on a {\it bipartite} square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence bond spin liquid state, interpolating the two different AF ordered states in the large $J_{1}$ and large $J_{2}$ limits, respectively. This novel spin liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structu…
Double quantum dot nanostructures embedded between two superconducting leads or in a superconducting ring have complex excitation spectra inside the gap which reveal the competition between different many-body phenomena. We study the corresponding two-impurity Anderson model using the non-perturbative numerical renormalization group (NRG) technique and identify the characteristic features in the spectral function in various parameter regimes. At half-filling, the system always has a singlet ground state. For large hybridization, we observe an inversion of excited inter-dot triplet and singlet …
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
Motivated by a recent experiment on Rb2Cu3SnF12, where spin-1/2 Cu2+ moments reside on the layers of Kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed Kagome lattices. The deformation is characterized by a weaker exchange coupling (alpha*J) on certain lattice links appropriate for Rb2Cu3SnF12 with alpha=1 corresponding to the ideal Kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operato…
A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations o…
We present an Ising-like intermediate phase for one-dimensional Kondo insulator systems. Resulting from a spinon splitting, its low-energy excitations are critical Ising modes, whereas the triplet sector has a spectral gap. It should occur as long as the RKKY oscillation amplitude dominates over any direct exchange between localized spins. The chiral fixed point, however, becomes unstable in the far Infra-Red limit due to prevalent fluctuations among localized spins which induce gapless triplet excitations in the spectrum. Based on previous numerical results, we obtain a paramagnetic disordere…
Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
Natural faculty of Science, Langson college of education（朗山师范学院自然科学系）；Department of Theoretical Physics, VNUHCM-University of Science（越南国立大学胡志明市理工大学理论物理系）；Institute of Research and Development, Duy Tan University（戴南大学研发院）；Faculty of Natural Sciences, Duy Tan University（戴南大学自然科学学院）
We study the excitation spectrum of the two-chain S=1/2 Heisenberg spin ladder with additional inter-chain second-neighbor frustrating interactions. The one and two-particle excitations are analyzed by using a mapping of the model onto a Bose gas of hard-core triplets. We find that low-lying singlet and triplet two-particle bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by a combination of variational and exact diagonalization techniques. We prove that the larger the number of bound quasiparticles the l…
We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1…
We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound SmB$_6$. Within a combination of the local density approximation (LDA) and an exact diagonalization (ED) of an effective discrete Anderson impurity model, the intermediate valence ground state with the $f$-shell occupation $\langle n_{4f} \rangle=5.6$ is found for the Sm atom in SmB$_6$. This ground state is a singlet, and the first excited triplet state $\sim 3$ meV higher in the energy. SmB$_6$ is a narrow band insulator already in LDA, with the direct band gap of $\sim 10$ meV. The …
