scholarly journals Professor Chen Ping Yang’s early significant contributions to mathematical physics

2019 ◽  
Vol 33 (06) ◽  
pp. 1930002
Author(s):  
Xi-Wen Guan ◽  
Feng He
Keyword(s):  
Statistical Mechanics ◽  
Spin Chain ◽  
Lattice Gas ◽  
Quantum Statistical Mechanics ◽  
Delta Function ◽  
Mathematical Physics ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Wide Range ◽  
Chen Ning Yang

In the 60s Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe’s hypothesis for various problems of physics. The works on the lattice gas model, critical behavior in liquid–gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe’s hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.

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

The topological basis expression of Heisenberg spin chain

2013 ◽  
Vol 13 (2) ◽  
pp. 401-414 ◽  
Author(s):  
Taotao Hu ◽  
Hang Ren ◽  
Kang Xue
Keyword(s):  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

A Riemann-Hilbert Approach to Discrete Heisenberg-Spin Chain

1989 ◽  
Vol 58 (3) ◽  
pp. 817-820 ◽  
Author(s):  
A. Roy Chowdhury ◽  
Mrityunjoy De
Keyword(s):  
Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain
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