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 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

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 Dynamic Correlation Functions for Quantum Spin Chains

1983 ◽  
Vol 51 (3) ◽  
pp. 219-222 ◽  
Author(s):  
Gerhard Müller ◽  
Robert E. Shrock
Keyword(s):  
Correlation Functions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Dynamic Correlation

THE TENSOR PRODUCT OF TENSOR OPERATORS OVER QUANTUM ALGEBRAS: SOME APPLICATIONS TO QUANTUM SPIN CHAINS

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3655-3669
Author(s):  
M. SCHEUNERT
Keyword(s):  
Tensor Product ◽  
Correlation Functions ◽  
Recent Article ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Algebras ◽  
Quantum Spin Chains ◽  
Expectation Values ◽  
Point Correlation ◽  
Tensor Operators

The present work is a direct sequel to a recent article by the author, in which he has analysed the tensor product of tensor operators over quantum algebras. Here the results obtained there are summarized and then specialized and extended to prepare possible applications to quantum spin chains. In particular, certain invariant two-point operators are introduced (whose expectation values yield the invariant two-point correlation functions) and their multiplicative properties are derived.

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.

scholarly journals FUSED POTTS MODELS

1993 ◽  
Vol 08 (29) ◽  
pp. 5165-5233 ◽  
Author(s):  
W.M. KOO ◽  
H. SALEUR
Keyword(s):  
Phase Diagram ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Valence Bond ◽  
Quantum Spin ◽  
Transition Line ◽  
Vertex Model ◽  
Quantum Spin Chain ◽  
General Technique ◽  
Potts Models

Generalizing the mapping between the Potts model with nearest neighbor interaction and the six-vertex model, we build a family of “fused Potts models” related to the spin k/2 U q su (2) invariant vertex model and quantum spin chain. These Potts models still have variables taking values 1, …,Q[Formula: see text] but they have a set of complicated multispin interactions. The general technique to compute these interactions, the resulting lattice geometry, symmetries, and the detailed examples of k=2, 3 are given. For Q>4, spontaneous magnetizations are computed on the integrable first order phase transition line, generalizing Baxter’s results for k=1. For Q≤4, we discuss the full phase diagram of the spin 1 (k=2) anisotropic and U q su (2) invariant quantum spin chain [it reduces in the limit Q=4 (q=1) to the much studied phase diagram of the isotropic spin 1 quantum spin chain], Several critical lines and massless phases are exhibited. The appropriate generalization of the valence bond state method of Affleck et al. is worked out.

Sign in / Sign up

Export Citation Format

Share Document