By means of a variational calculation using Matrix Product States with periodic boundary conditions, we accurately determine the extension of the spin-supersolid phase predicted to exist in the spin-1 anisotropic Heisenberg chain. We compute both the structure factor and the superfluid stiffness, and extract the critical exponents of the supersolid-to-solid phase transition.
We use quantum Monte Carlo methods to demonstrate that the quantum phase diagram of the S=1 Heisenberg model with uniaxial anisotropy contains an extended supersolid phase. We also show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low energy spectrum of a class of {\it isotropic} and {\it frustrated} spin systems. This crucial result provides the required guidance for finding experimental realizations of a spin supersolid state.
The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds $A_2$CoTeO$_6$ ($A$ = Ca, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in …
We consider an S=1 Heisenberg chain with strong exchange (Delta) and single--ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low energy sectors for a given window of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering that coexists with the finite spin stiffness obtained from the exact solution of the effective XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagr…
We study the spin-3/2 Heisenberg model including easy-plane and exchange anisotropies in one and two dimensions. In the Ising limit, when the off-diagonal exchange interaction J is zero, the phase diagram in magnetic field is characterized by magnetization plateaus that are either translationally invariant or have a two-sublattice order, with phase boundaries that are macroscopically degenerate. Using a site factorized variational wave function and perturbational expansion around the Ising limit, we find that superfluid and supersolid phases emerge between the plateaus for small finite values …
We use a quantum Monte Carlo method to study the ground state and thermodynamic phase transitions of the spin supersolid phase in the S=1 Heisenberg model with uniaxial anisotropy. The thermal melting of the supersolid phase shows unqiue signatures in experimentally measurable observables. This Hamiltonian is a particular case of a more general and ubiquitous model that describes the low energy spectrum of a class of {\it isotropic} and {\it frustrated} spin systems. We also discuss some alternative realizations of spin supersolid states in real magnets.
The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO 2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbour interactions and single-ion easy-axis anisotropy. Using a combination of classical M…
Motivated by numerical evidence of the valence bond groundstate of the two-dimensional Heisenberg pyrochlore lattice, we argue using a $t$-$J$ model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-$T_c$ cuprates as well as possible relevance to frustrated noncuprate superconductors such as …
We study the Heisenberg antiferromagnet on the Shastry-Sutherland lattice under magnetic fields, to clarify the magnetic properties of SrCu_2(BO_3)_2. Treating magnetic excitations promoted by the field as Bose particles and using strong coupling expansion, we derive an effective Hamiltonian for the effective magnetic particles. Anisotropic repulsive interactions between effective particles induce `insulating' states with a stripe SDW structure at magnetization m/m_{sat}=1/3 and a checkerboard structure at 1/2, and thereby form magnetization plateaus. Supersolid phases appear around insulating…
We demonstrate that low-lying triplon excitations in a bilayer Heisenberg antiferromagnet provide a promising avenue to realize magnetic analogs of twisted superfluid and supersolid phases that were recently reported for two-component ultracold atomic condensate in an optical lattice. Using a cluster Gutzwiller mean-field theory, we establish that Dzyaloshinskii-Moriya interactions (DMI), that are common in many quantum magnets, stabilize these phases in a magnetic system, in contrast to the pair hopping process that is necessary for ultracold atoms. The critical value of DMI for transition to…
In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L * L square lattice with periodic boundary conditions and nearest neighbor hopping.
We construct a Ginsburg Landau (GL) theory to study the phases of liquid, solid, superfluid, especially a possible supersolid and phase transitions among these phases in a unified framework. In this GL, we put the two competing orders between the solid component and the superfluid component on the same footing. We only introduce two parameters: $ v $ which is the repulsive interaction between the normal component and the local superfluid mode and $ g $ which is a periodically changing chemical potential for the local superfluid mode. The microscopic origins of $ v $ and $ g $ are given. By usi…
Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所物质结构理论研究中心）；School of Physics, Beihang University（北京航空航天大学物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute (PRI)（理化学所先锋研究本部）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力研究机构先进科学研究中心）
We study the fate of interacting quantum systems which are periodically driven by switching back and forth between two integrable Hamiltonians. This provides an unconventional and tunable way of breaking integrability, in the sense that the stroboscopic time evolution will generally be described by a Floquet Hamiltonian which progressively becomes less integrable as the driving frequency is reduced. Here, we exemplify this idea in spin chains subjected to periodic switching between two integrable anisotropic Heisenberg Hamiltonians. We distinguish the integrability-breaking effects of resonant…
We study the spin-$1$ model in a triangular lattice in presence of a uniaxial anisotropy field using a Cluster Mean-Field approach (CMF). The interplay between antiferromagnetic exchange, lattice geometry and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF yields two supersolid (SS) phases compatible with those present in the spin-$1/2$ XXZ model onto which the spin-$1$ system maps. Between these two SS phases, the three-sublattice order is broken and the results of the CMF depend heavily on the geometry and size of the cluste…
Dipolar and quadrupolar spin supersolid states in a spin-1 triangular antiferromagnet
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所物质结构研究センター）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学研究中心）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算研究中心）；RIKEN Pioneering Research Institute (PRI)（理化学研究所开创性研究所）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力机构先进科学研究中心）
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size …
Bipartite entanglement measures are fantastic tools to investigate quantum phases of correlated electrons. Here, I analyze the entanglement spectrum of **gapped** two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains. Comparison of various entanglement entropies proposed in the literature is given. The entanglement spectrum is shown to closely reflect the low-energy gapless spectrum of each individual edge, for any sign of the exchange coupling constants. This extends the conjecture initially drawn for Fractional Quantum Hall systems to the fiel…
We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bos…
We present a dynamical mean-field study of two-particle dynamical response functions in two-band Hubbard model across several phase transitions. We observe that the transition between theexcitonic condensate and spin-state ordered state is continuous with a narrow strip of supersolidphase separating the two. Approaching transition from the excitonic condensate is announced bysoftening of the excitonic mode at theMpoint of the Brillouin zone. Inside the spin-state orderedphase there is a magnetically ordered state with 2x2 periodicity, which has no precursor in thenormal phase.
We have succeeded in synthesizing single crystals of the verdazyl radical beta-2,6-Cl2-V [= beta-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl]. The ab initio MO calculation indicated the formation of an S = 1/2 Heisenberg antiferromagnetic chain with four-fold magnetic periodicity consisting of three types of exchange interactions.We have successfully explained the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we revealed that the alternating and unique Ising ferromagnetic chains become effective in the specific fiel…
We performed variational calculation based on the multi-scale entanglemnt renormalization ansatz, for the antiferromagnetic Heisenberg model on a Shastry Sutherland lattice (SSL). Our results show that at coupling ratio J'/J= 0.687(3), the system undergoes a quantum phase transition from the orthogonal dimer order to the plaquette valence bond solid phase, which then transits into the antiferromagnetic order above J'/J=0.75. In the presence of an external magnetic field, our calculations show clear evidences of various magnetic plateaux in systems with different coupling ratios range from 0.5 …
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain of N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D^3, where g(D,ξ/N) is a nontrivial function. For ξ<< N, this scaling reduces to D^3, independent of the system size N, making our algorithm N times faster than previous proposal…
As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detect phase transitions accompanied with periodicity change, where the incommensurate MPS is generated by acting local-spin-rotation operators with the incommensurate periodicity on a uniform MPS. As a commensurate/commensurate change, we calculate the partial ferro -- perfect ferro phase transition in the $S=1/2$ Heisenberg model and its critical exponent of the magnetization curve. As a commensurate/incommensurate change, we calculate the S=1 Heisenberg model with bilinear …
We study three-leg antiferromagnetic Heisenberg model with the periodic boundary conditions in the rung direction. Since the rungs form regular triangles, spin frustration is induced. We use the density-matrix renormalization group method to investigate the ground state. We find that the spin excitations are always gapped to remove the spin frustration as long as the rung coupling is nonzero. We also visibly confirm spin-Peierls dimerization order in the leg direction. Both the spin gap and the dimerization order are basically enhanced as the rung coupling increases.
When Heisenberg spins interact antiferromagnetically on a triangular lattice and nearest-neighbor interactions dominate, the ground state is 120$^{\circ}$ antiferromagnetism. In this work, we probe the response of this state to lifting the triangular symmetry, through investigation of the triangular antiferromagnet PdCrO$_2$ under uniaxial stress by neutron diffraction and resistivity measurements. The periodicity of the magnetic order is found to change rapidly with applied stress; the rate of change indicates that the magnetic anisotropy is roughly forty times the stress-induced bond length …
We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field $h_{3}$ and a small periodic field of strength $h_{1}$. For the case of a transverse staggered field a gap opens, which scales with $h_{1}^{ε_{1}}$, where $ε_{1}=ε_{1}(h_{3})$ is given by the critical exponent $η_{1}(M(h_{3}))$ defined through the transverse structure factor of the model at $h_{1}=0$. For the case of a longitudinal periodic field with wave vector $q=π/2$ and strength $h_{q}$ a plateau is found in the magnetization curve at $M=1/…
We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
The $S=1$ antiferromagnetic Heisenberg model on a Kagome lattice is studied using the density-matrix renormalization group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal singlet solid (HSS) and triangular valence bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy par sites of the HSS state is $e_0=E_0/N =-1.41095$, which is readily lower than that of the TVBS state ($e_0=-1.3912 \pm 0.0025$). This agrees well with those of the cyli…
A model of mobile-bond defects is tentatively proposed to analyze the "anomalies" observed on the NMR spectrum of the quantum Heisenberg chains of Sr2CuO3. A bond-defect is a local change in the exchange coupling. It results in a local alternating magnetization (LAM), which when the defect moves, creates a flipping process of the local field seen by each nuclear spin. At low temperature, when the overlap of the LAM becomes large, the defects form a periodic structure, which extends over almost all the chains. In that regime, the density of bond-defects decreases linearly with T.
We examine ground state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that besides Neel order harbors regions of extensive ground state degeneracy. In the quantum regime, we find a dimerized phase of triplet states, separated from the Neel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization proc…
Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents $p_α^{(p)}$ and $p_α^{(o)}$ that gives the power-law decay of the oscillations of the $α-$Renyi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger paramet…
Entanglement renormalization techniques are applied to numerically investigate the ground state of the spin-1/2 Heisenberg model on a kagome lattice. Lattices of N={36,144,inf} sites with periodic boundary conditions are considered. For the infinite lattice, the best approximation to the ground state is found to be a valence bond crystal (VBC) with a 36-site unit cell, compatible with a previous proposal. Its energy per site, E=-0.43221, is an exact upper bound and is lower than the energy of any previous (gapped or algebraic) spin liquid candidate for the ground state.
We present the results of exact diagonalization calculations of the isolated and isothermal on-site static susceptibilities in the anisotropic extended Heisenberg model on a linear chain with periodic boundary conditions. Based on the ergodicity considerations we conclude that the isothermal susceptibility will diverge as $T\to 0$ both in finite clusters and in the bulk system in two non-ergodic regions of the phase diagram of the system.
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa$_2$S$_4$. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained …
For a class of quasi-one-dimensional clusters, by using exact diagonalization, we study the effect of side spins on the spin-spin correlations on chain. Our calculations show that the side spins added in the same sublattice can effectively strengthen the spin-spin correlations in large distance region and make the change tend to flat. It is exactly proved that periodically adding side spins can set up magnetic long-range orders in the ground state. Also we investigate the effect of the density of side spins on correlation strength. The case that two sublattices have different localized spins i…
We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_α,J_β,J_γ)$ on bonds …
We analyze the finite-size scaling of the average gap-ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin-chain with quasi-periodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of Berezinskii-Kosterlitz-Thouless (BKT) transition, the same as in the case of uniformly disordered systems as advocate…
We study the entanglement spectrum (ES) of a finite XXZ spin 1/2 chain in the limit Δ-> -1^+ for both open and periodic boundary conditions. At Δ=-1 (ferromagnetic point) the model is equivalent to the Heisenberg ferromagnet and its degenerate ground state manifold is the SU(2) multiplet with maximal total spin. Any state in this so-called "symmetric sector" is an equal weight superposition of all possible spin configurations. In the gapless phase at Δ>-1 this property is progressively lost as one moves away from the Δ=-1 point. We investigate how the ES obtained from the states in this manifo…
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size perio…
We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with Möbius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the Möbius boundary provides the clear evidence of the single spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spino…
We presents the results of an extensive numerical study of the phase diagram of the spin-1/2, \protect{$J_1$-$J_2$-$J_3$} Heisenberg model on a square lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor interactions $J_1$, using exact diagonalization with periodic and twisted boundary conditions. Comparison is made with published spin wave calculations. We show that quantum fluctuations play a very important role, changing both the extent and the wave vector of classical spiral phases, and leading to new quantum phases where the classical spiral states have a high degeneracy…
The relevance of zero-energy functions, coming from zero-energy modes and present in the structure of bosonic Green's functions, is often underestimated. Usually, their values are fixed by assuming the ergodicity of the dynamics, but it can be shown that this is not always correct. As the zero-energy functions are connected to fundamental response properties of the system under analysis (specific heat, compressibility, susceptibility, etc.), their correct determination is not an irrelevant issue. In this paper we present some results regarding the zero-energy functions for the Heisenberg chain…
We study formation of a periodical structure of quasiparticle-like magnetic configurations with non-trivial topological charge, known as a magnetic skyrmion phase, on a frustrated triangular lattice antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya interaction (DMI) by means of Monte Carlo simulations. The existence of such a phase, formed on the three interpenetrating sublattices, has been demonstrated for a sufficiently large strength of DMI. The goal of the present investigation is to establish the minimum values of both the DM interaction strength as well as the magnetic field …
