scholarly journals Spin chains with boundary inhomogeneities

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Rafael I. Nepomechie ◽  
Ana L. Retore
Keyword(s):  
Quantum Group ◽  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Spin Chains ◽  
Group Symmetry ◽  
Quantum Spin Chain ◽  
Open Quantum ◽  
Bethe Ansatz Solution

Abstract We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.

Bethe ansatz solution of the Fateev-Zamolodchikov quantum spin chain with boundary terms

1990 ◽  
Vol 147 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Luca Mezincescu ◽  
Rafael I. Nepomechie ◽  
V. Rittenberg
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Boundary Terms ◽  
Bethe Ansatz Solution

Six-Vertex Model

2019 ◽  
pp. 454-473
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Square Lattice ◽  
Vertex Model ◽  
Quantum Spin Chain ◽  
Special Value ◽  
Quantum Operators ◽  
The One

This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter relations, the six-vertex model is diagonalized and the Bethe ansatz equations are derived. The Hamiltonian of the Heisenberg quantum spin chain is obtained from the transfer matrix for a special value of the spectral parameter together with an infinite set of further conserved quantum operators. By the diagonalization of the transfer matrix the exact solution of the one-dimensional quantum spin chain Hamiltonian has automatically also been obtained, which is given by the same Bethe ansatz equations.

scholarly journals Quantum spin chains with quantum group symmetry

1996 ◽  
Vol 174 (3) ◽  
pp. 477-507 ◽  
Author(s):  
M. Fannes ◽  
B. Nachtergaele ◽  
R. F. Werner
Keyword(s):  
Quantum Group ◽  
Quantum Spin ◽  
Spin Chains ◽  
Group Symmetry ◽  
Quantum Spin Chains

scholarly journals INTEGRABILITY OF OPEN SPIN CHAINS WITH QUANTUM ALGEBRA SYMMETRY

1991 ◽  
Vol 06 (29) ◽  
pp. 5231-5248 ◽  
Author(s):  
LUCA MEZINCESCU ◽  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Spin Chain ◽  
Quantum Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Invariant Chain ◽  
Quantum Spin Chain ◽  
Fundamental Representation ◽  
R Matrix ◽  
Boundary Terms ◽  
Xxz Chain

We construct an open quantum spin chain from the “twisted” [Formula: see text]R matrix in the fundamental representation which has the quantum algebra symmetry Uq[ su (2)]. This anisotropic spin-1 chain is different from the Uq[ su (2)]-invariant chain constructed from the “untwisted” [Formula: see text] spin-1 R matrix (namely, the spin-1 XXZ chain of Fateev-Zamolodchikov with boundary terms) but, nevertheless, is also completely integrable. We discuss the general case of an R matrix of the type g(k), where k∈{1, 2, 3}, and g is any simple Lie algebra.

scholarly journals BETHE ANSATZ SOLUTIONS FOR TEMPERLEY–LIEB QUANTUM SPIN CHAINS

2000 ◽  
Vol 15 (21) ◽  
pp. 3395-3425 ◽  
Author(s):  
R. C. T. GHIOTTO ◽  
A. L. MALVEZZI
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Free Boundary Conditions

We solve the spectrum of quantum spin chains based on representations of the Temperley–Lieb algebra associated with the quantum groups [Formula: see text] for Xn=A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

scholarly journals Bethe ansatz on a quantum computer?

2021 ◽  
Vol 21 (3&4) ◽  
pp. 255-265
Author(s):  
Rafael I. Nepomechie
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Quantum Computer ◽  
Quantum Spin ◽  
Variational Parameter ◽  
Quantum Spin Chain

We consider the feasibility of studying the anisotropic Heisenberg quantum spin chain with the Variational Quantum Eigensolver (VQE) algorithm, by treating Bethe states as variational states, and Bethe roots as variational parameters. For short chains, we construct exact one-magnon trial states that are functions of the variational parameter, and implement the VQE calculations in Qiskit. However, exact multi-magnon trial states appear to be out out of reach.

scholarly journals A SPIN CHAIN PRIMER

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2973-2985 ◽  
Author(s):  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Quantum Spin ◽  
Baxter Equation ◽  
Quantum Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Chain Primer

This is a very elementary introduction to the Heisenberg (XXX) quantum spin chain, the Yang–Baxter equation, and the algebraic Bethe Ansatz.

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