scholarly journals Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

1995 ◽  
Vol 52 (6) ◽  
pp. 4319-4326 ◽  
Author(s):  
Joachim Stolze ◽  
Angela Nöppert ◽  
Gerhard Müller
Keyword(s):  
Power Law ◽  
Correlation Functions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Time Dependent ◽  
Quantum Spin Chains ◽  
Power Law Decay ◽  
Dependent Correlation

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.

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
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