547 citations · 2.8k across the 92 of their papers we have counts for
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Exceptional Points in the Baxter-Fendley Free Parafermion Model
Robert A. Henry, Murray T. Batchelor
Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a…
A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
Remy Adderton, Murray T. Batchelor, Paul Wedrich
The hamiltonian of the -state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by types of Temperley-Lieb generators. This genera…
Some ground-state expectation values for the free parafermion Z(N) spin chain
Zi-Zhong Liu, Robert A. Henry, Murray T. Batchelor +1
We consider the calculation of ground-state expectation values for the non-Hermitian Z(N) spin chain described by free parafermions. For N=2 the model reduces to the quantum Ising…
Anomalous bulk behaviour in the free parafermion spin chain
Francisco C. Alcaraz, Murray T. Batchelor
We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple model for…
Energy spectrum and critical exponents of the free parafermion spin chain
Francisco C Alcaraz, Murray T Batchelor, Zi-Zhong Liu
Results are given for the ground state energy and excitation spectrum of a simple -state spin chain described by free parafermions. The model is non-Hermitian for $N \ge 3…
Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
Yan-Wei Dai, Sam Young Cho, Murray T. Batchelor +1
The von Neumann entanglement entropy is used to estimate the critical point of the mixed ferro-antiferromagnetic three-state quantum Potts model $H = \sum_i…
Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday
Murray T Batchelor, Vladimir V Bazhanov, Vladimir V Mangazeev
This is an introduction to Exactly Solved Models and Beyond, a special issue collection of articles published in J. Phys. A in honour of R J Baxter's 75th birthday.
Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
Murray T. Batchelor, Angela Foerster
The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number…
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
Qian-Qian Shi, Huan-Qiang Zhou, Murray T. Batchelor
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the -orthogonality of a few near-dege…
Scaling and universality in the 2D Ising model with a magnetic field
Vladimir V. Mangazeev, Michael Yu. Dudalev, Vladimir V. Bazhanov +1
The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approac…
Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions
X. W. Guan, M. T. Batchelor, C. Lee +1
Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transiti…
Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization
J. -S. He, A. Foerster, X. W. Guan +1
An extensive investigation is given for magnetic properties and phase transitions in one-dimensional Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means…
Variational approach to the scaling function of the 2D Ising model in a magnetic field
Vladimir V. Mangazeev, Murray T. Batchelor, Vladimir V. Bazhanov +1
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high prec…
Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
X. -W. Guan, M. T. Batchelor, J. -Y. Lee
We investigate magnetic properties and statistical effects in 1D strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons.…
One-dimensional anyons with competing -function and derivative -function potentials
M. T. Batchelor, X. -W. Guan, A. Kundu
We propose an exactly solvable model of one-dimensional anyons with competing -function and derivative -function interaction potentials. The Bethe ansatz equations are derive…
Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions
X. W. Guan, M. T. Batchelor, C. Lee +1
We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact resul…
Ferromagnetic behaviour in the strongly interacting two-component Bose gas
X. -W. Guan, M. T. Batchelor, M. Takahashi
We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the character…
Bethe Ansatz for 1D interacting anyons
M. T. Batchelor, X. -W. Guan, J. -S. He
This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Beth…
Generalized exclusion statistics and degenerate signature of strongly interacting anyons
M T Batchelor, X W Guan
We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal parti…
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
M. T. Batchelor, M. Bortz, X. W. Guan +1
We investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Anal…
Theoretical analysis of the double spin chain compound KCuCl_3
M. T. Batchelor, X. W. Guan, N. Oelkers
We investigate thermal and magnetic properties of the double spin chain compound KCuCl_3 via an exactly solved ladder model with strong rung interaction. Results from the analysis…
Exact results for the 1D interacting mixed Bose-Fermi gas
M. T. Batchelor, M. Bortz, X. W. Guan +1
The exact solution of the 1D interacting mixed Bose-Fermi gas is used to calculate ground-state properties both for finite systems and in the thermodynamic limit. The quasimomentum…
The 1D Bose Gas with Weakly Repulsive Delta Interaction
M T Batchelor, X-W Guan, C Dunning +1
We consider the asymptotic solutions to the Bethe ansatz equations of the integrable model of interacting bosons in the weakly interacting limit. In this limit we establish that th…
Ground state of one-dimensional bosons with delta interaction: link to the BCS model
M. T. Batchelor, X. W. Guan, J. B. McGuire
The Bethe roots describing the ground state energy of the integrable 1D model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of…