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International Journal of Quantum Chemistry

Quantum‐phase transitions in 1D Heisenberg spin systems

Vladyslav O. Cheranovskii, Victor V. Slavin, Douglas J. Klein

Published Oct 15, 2020• 7 citations
Publisher

Abstract

Abstract Focusing on novel highly correlated low‐dimensional systems, we investigate a class of quasione‐dimensional systems with an even number of spin‐½ sites per unit cell, for which we find, here, that it does not give a gap in the exact excitation spectrum. The unit cells of these systems are formed by two different structural units, each with an odd number of sites. We find the instability of these systems against the regular oscillations of the interactions between structural units and estimate numerically the corresponding critical exponents for the ground‐state energies. In contrast to the well‐known spin‐Peierls instability, this type of structural instability does not change the symmetry of the above systems. We also present a class of disordered one‐dimensional spin systems formed by different types of structural units with odd numbers of spins to demonstrate a critical behavior similar to a homogeneous spin‐½ chain in the limit of weak interactions between structural units.

DOI
10.1002/qua.26498

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•Mar 24, 2015•2 citations
Abstract Focusing on novel highly correlated low‐dimensional systems, we investigate a class of quasione‐dimensional systems with an even number of spin‐½ sites per unit cell, for which we find, here, that it does not give a gap in the exact excitation spectrum. The unit cells of these systems are formed by two different structural units, each with an odd number of sites. We find the instability of these systems against the regular oscillations of the interactions between structural units and estimate numerically the corresponding critical exponents for the ground‐state energies. In contrast to the well‐known spin‐Peierls instability, this type of structural instability does not change the symmetry of the above systems. We also present a class of disordered one‐dimensional spin systems formed by different types of structural units with odd numbers of spins to demonstrate a critical behavior similar to a homogeneous spin‐½ chain in the limit of weak interactions between structural units.
A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered.
We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents p of spin-Peierls transition of above spin systems on the value of J. In contrast to chain systems, we find significantly non-monotonous dependence p (J) for three-legs ladder system. In the limit of weak coupling J we derive effective spin s chain Hamiltonians describing the low-energy states of the system considered by means of perturbation theory. The value of site spin s coincides with the value of the ground-state spin of the isolated unit cell of the system considered. This means that at small J values all the systems with the singlet ground state and the same half-integer value of s should have a similar critical behavior which is in agreement with our numerical study. The presence of gapped excitations inside the unit cells at small values of J should give, for our spin systems, at least one intermediate plateau in field dependence of magnetization at low temperatures. The stability of this plateau against the increase of the values of J and temperature is studied using the quantum Monte-Carlo method.
Abstract The exact diagonalization (ED) approach and Quantum Monte-Carlo (QMC) method were used for the study of the lowest energy states and low-temperature magnetic properties of some disordered 1D Heisenberg spin-1/2 systems formed by two types of three-spin structural units. For the system with a singlet ground state and the random distribution of structural units along the chain system, a significant decrease of the size of the intermediate magnetization plateau in comparison to the corresponding uniform spin system was found. For the “polyallyl” spin chain with a macroscopic value of the ground state spin, a transition to the singlet ground state due to the effect of compositional disorder was observed.
Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors.The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts.In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin S A 2  of odd or even-numbered sites is discontinuous.There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous S A 2 .Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.(
We investigate the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model with a $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo method, we obtain the properties of the nonplateau XY phase; 1/9, 3/9, 5/9, and 7/9 magnetization plateau phases; and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the three-dimensional XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the nonplateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part due to the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory of the effective ``block spin'' model in the canted antiferromagnetic phase. In the magnetization plateau phase, we identify that the low-energy excitations arise from the localized disturbances within the sublattice and are capable of spreading in momentum space. The high-energy quasiparticles could be the multiplet excitations similar to the ``triplon'' in the dimerized system and ``doublon'' and ``quarton'' in the trimerized system. This paper offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectra in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with odd-spin configurations in the checkerboard unit cells under the influence of a longitudinal magnetic field.
We investigate disordered phases realized in one-dimensional quantum spin systems.We revisit an effective field theory proposed by Schulz [Phys.Rev. B 34, 6372 (1986)], which encapsulates several essential properties in low energy, from the point of view of symmetry.Although this effective theory was originally derived by perturbation theory, we find that it is fully consistent with the symmetry of the Hamiltonian and thus uniquely identified in the non-perturbative sense.This theory explains many possible phase transitions known to occur among valence-bond-solid phases, which are typical disordered phases in one-dimensional spin systems.Furthermore, this theory indicates that the phase transitions only occur under one of four symmetries: time reversal, bond-centered inversion, dihedral group of spin rotations, and site-centered inversion combined with a spin rotation.Surprisingly, the first three symmetries are consistent with those protecting the Haldane phase in spin-1 chains, which have already been found by a completely different approach using the matrix-product state (MPS).On the other hand, the last one is not known so far.To understand it, we explicitly construct a microscopic model that has two distinct disordered phases protected by the combined inversion symmetry.We examine this model and confirm the existence of those disordered phases by perturbation theory and numerical simulations.For completeness, we further give a more rigorous proof of their existence, based on the non-translation-invariant MPS.We also propose an extension of the Lieb-Schultz-Mattis theorem for the absence of a unique gapped ground state in half-odd-integer spin systems with site-centered inversion symmetry.