scholarly journals How to Draw a Correlation Function

2021 ◽  
Author(s):  
Nikolay Bogoliubov ◽  
◽  
Cyril Malyshev ◽  
Keyword(s):  
Correlation Functions ◽  
Symmetric Functions ◽  
Scaling Limit ◽  
Wave Functions ◽  
Lattice Paths ◽  
Enumerative Combinatorics ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Auto Correlation ◽  
Combinatorial Derivation

We discuss connection between the XX0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combinatorial derivation of the dynamical auto-correlation functions and visualise them in terms of nests of self-avoiding lattice paths. Asymptotics of the auto-correlation functions are obtained in the double scaling limit provided that the evolution parameter is large.

scholarly journals Bethe state norms for the Heisenberg spin chain in the scaling limit

2019 ◽  
Vol 947 ◽  
pp. 114748 ◽  
Author(s):  
Gleb A. Kotousov ◽  
Sergei L. Lukyanov
Keyword(s):  
Spin Chain ◽  
Scaling Limit ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

scholarly journals Statistics of correlation functions in the random Heisenberg chain

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Luis A. Colmenarez ◽  
Paul A. McClarty ◽  
Masud Haque ◽  
David J. Luitz
Keyword(s):  
Correlation Functions ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Spin Flip ◽  
Local Operators ◽  
Many Body Systems ◽  
Degenerate Perturbation Theory

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) – at least in one dimensional systems – leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder – in the thermal phase – we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in S_i^z S_{i+r}^zSizSi+rz correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the S_i^zS_{i+r}^zSizSi+rz correlator exhibits striking differences between the MBL and Anderson insulator cases.

scholarly journals Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Charles B. Thorn
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Spin Chain ◽  
Discrete Dynamical System ◽  
Heisenberg Spin ◽  
Free Fermions ◽  
Heisenberg Spin Chain ◽  
Delta Sigma ◽  
Special Cases ◽  
Quantized String

Abstract Although the energy spectrum of the Heisenberg spin chain on a circle defined by$$ H=\frac{1}{4}\sum \limits_{k=1}^M\left({\sigma}_k^x{\sigma}_{k+1}^x+{\sigma}_k^y{\sigma}_{k+1}^y+\Delta {\sigma}_k^z{\sigma}_{k+1}^z\right) $$ H = 1 4 ∑ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether M ∈ 4ℕ + r, where r = −1, 0, 1, 2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M1< M and M − M1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case ∆ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R0. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for ∆ ≠ 0 is a change in the compactification radius R0→ R∆. As ∆ → −1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

scholarly journals Magnetic properties of theS= ½ Heisenberg spin-chain material (6MAP)CuCl3

2009 ◽  
Vol 150 (4) ◽  
pp. 042159 ◽  
Author(s):  
M Ozerov ◽  
E Čižmár ◽  
J Wosnitza ◽  
S A Zvyagin ◽  
F Xiao ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain
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