A TEMPLATE FOR QUANTUM SPIN CHAIN SPECTRA

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 707-730 ◽  
Author(s):  
PAUL MARTIN ◽  
VLADIMIR RITTENBERG
Keyword(s):  
Spin Chain ◽  
Hecke Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Irreducible Representations ◽  
Quantum Spin Chains ◽  
Young Diagrams ◽  
Quantum Spin Chain ◽  
Fixed Length

We consider a series of N-state L(≥N) site quantum spin chains, characterised by the ordered partition of N into 2 parts, N=P+M. These (P/M) chains are invariant under an action of UqSU(P/M), and are built from a representation of the Hecke algebra HL-1(q). We establish that the intersection of the spectra of a (P/M) and (P'/M') chain of fixed length L is the spectrum of the (min(P,P')/min(M,M')) chain of that length. We establish that the spectrum of the (P/M) chain breaks into blocks corresponding to irreducible representations of HL-1(q) (or equivalently irreducible representations of UqSU(P/M)) characterised by Young diagrams with no rectangular subdiagrams of dimension (P+1)×(M+1) (height × width resp.). We give the corresponding quotient relations for the Hecke algebra. We discuss several implications of these results.

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 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.

scholarly journals Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

2017 ◽  
Vol 3 (5) ◽  
Author(s):  
Michel Bauer ◽  
Denis Bernard ◽  
Tony Jin
Keyword(s):  
Spin Chain ◽  
Quantum Dynamics ◽  
Quantum Noise ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Dissipative Effects ◽  
Macroscopic Fluctuation Theory

Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.

CORRELATION FUNCTIONS IN QUANTUM SPIN CHAINS AND VERTEX MODELS

2001 ◽  
Vol 16 (11) ◽  
pp. 1875-1887
Author(s):  
VIERI MASTROPIETRO
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Quantum Spin ◽  
Spin Chains ◽  
Vertex Model ◽  
Quantum Spin Chains ◽  
Neighbor Interaction ◽  
Vertex Models

Some correlation functions of critical models, like the anisotropic spin chain with nearest and next-to-nearest neighbor interaction, or the eight vertex model, are computed as a corollary of the study of the XYZ model in [2].

scholarly journals LEVEL 2 IRREDUCIBLE REPRESENTATIONS OF $U_q (\widehat{{\rm sl}}_2)$, VERTEX OPERATORS, AND THEIR CORRELATIONS

1994 ◽  
Vol 09 (25) ◽  
pp. 4449-4484 ◽  
Author(s):  
MAKOTO IDZUMI
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Integral Formula ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Irreducible Representations ◽  
Vertex Operators ◽  
Quantum Spin Chain ◽  
Level 2

Vertex operators associated with level 2 [Formula: see text] modules are explicitly constructed using bosons and fermions. An integral formula is derived for the trace of products of vertex operators. These results are applied to give n-point spin correlation functions of an integrable S = 1 quantum spin chain, extending an earlier work of Jimbo et al. for the case S = 1/2.

scholarly journals Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Jiaju Zhang ◽  
Pasquale Calabrese ◽  
Marcello Dalmonte ◽  
Mohammad Ali Rajabpour
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Trace Distance ◽  
The Difference ◽  
Reduced Density

We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten nn-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as \ell^{-2}ℓ−2 for large length of the interval \ellℓ. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models
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