Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Zoltán G Soos,S Ramasesha,Manoranjan Kumar

doi:10.5562/cca2324

Abstract

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 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 . Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Highlights

Phase transitions occur in the thermodynamic limit of interacting many-body systems
There are four simple limits: U = V = 0 is a Hückel or tight-binding band of width 4t that is readily solved for any size; U >> V > 0 has singly occupied sites, np = 1, and magnetic properties given by an Heisenberg antiferromagnet (HAF) with J1 = 4t2 / (U – V); the ground state (GS) for large V is a charge density wave (CDW) with doubly occupied sites on one sublattice and empty sites on the other; when both U and V are large, there is a first-order quantum transition at V ~ U / 2 between spin liquid and CDW
We have explored similarities among the quantum phase diagrams of three classes of 1D models with spaced sites: frustrated spin chains with variable range exchange, half-filled Hubbard models with spinindependent interactions and ionic or modified Hubbard models with site energies

Summary

INTRODUCTION

Phase transitions occur in the thermodynamic limit of interacting many-body systems. Thermodynamic phase transitions reflect competition between internal energy and entropy that depends on parameters such as temperature, pressure or volume. There are four simple limits: U = V = 0 is a Hückel or tight-binding band of width 4t that is readily solved for any size; U >> V > 0 has singly occupied sites, np = 1, and magnetic properties given by an HAF with J1 = 4t2 / (U – V); the GS for large V is a charge density wave (CDW) with doubly occupied sites on one sublattice and empty sites on the other; when both U and V are large, there is a first-order quantum transition at V ~ U / 2 between spin liquid and CDW. As discussed elsewhere,[13,32] the model with coupling to vibrations describes IR, optical and dielectric properties of CT crystals with continuous or firstorder neutral ionic transitions

Findings

DISCUSSION

CONCLUSION