# Equilibrium dynamics of the XX chain

@article{Ghmann2019EquilibriumDO, title={Equilibrium dynamics of the XX chain}, author={Frank G{\"o}hmann and Karol Kajetan Kozlowski and Jesko Sirker and Junji Suzuki}, journal={Physical Review B}, year={2019} }

The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion.
The transversal correlation function is evaluated in real time and space. The high-accuracy calculation reproduces several exact results in limiting cases as well as the well-known asymptotic formulas obtained by the matrix Riemann-Hilbert approach.
Furthermore, comparisons to numerical data based on a direct…

## 15 Citations

### Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

- PhysicsSciPost Physics
- 2022

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a…

### High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain

- MathematicsJournal of Mathematical Physics
- 2020

We analyse the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm…

### Low-temperature asymptotic of the transverse dynamical structure factor for a magnetically polarized XX chain

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

The Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida–Tserkovnikov algorithm. Starting…

### Effective free-fermionic form factors and the XY spin chain

- Physics
- 2020

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the…

### A thermal form factor series for the longitudinal two-point function of the Heisenberg–Ising chain in the antiferromagnetic massive regime

- PhysicsJournal of Mathematical Physics
- 2021

We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the…

### Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime

- PhysicsLetters in Mathematical Physics
- 2020

We derive an explicit expression for the leading term in the long-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This…

### Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime

- PhysicsLetters in Mathematical Physics
- 2020

We derive an explicit expression for the leading term in the long-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This…

### On the dynamics of free-fermionic tau-functions at finite temperature

- PhysicsSciPost Physics Core
- 2022

In this work we explore an instance of the
\tauτ-function
of vertex type operators, specified in terms of a constant phase shift
in a free-fermionic basis. From the physical point of view this…

### Analytical results for the low-temperature Drude weight of the XXZ spin chain

- PhysicsPhysical Review B
- 2021

The spin-1/2 XXZ chain is an integrable lattice model and parts of its spin current can be protected by local conservation laws for anisotropies −1 < ∆ < 1. In this case, the Drude weight D(T ) is…

### Large-time and long-distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas

- PhysicsPhysical Review B
- 2022

We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large…

## References

SHOWING 1-10 OF 127 REFERENCES

### Dynamical correlation functions of the XXZ model at finite temperature

- Physics
- 2007

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for…

### Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

- Physics
- 1993

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all…

### On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

- Physics
- 2009

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that…

### Spin spin correlation functions of the XXZ - 1/2 Heisenberg chain in a magnetic field

- Physics, Mathematics
- 2002

### Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

- Mathematics
- 2007

We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density…

### Hidden Grassmann structure in the XXZ model III: introducing the Matsubara direction

- Mathematics
- 2009

We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a…

### Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

- Physics
- 2016

We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic…

### Exact results for the dynamics of one-dimensional spin-systems

- Physics
- 1976

In this contribution we discuss the spin-dynamics of anisotropic one-dimensional spin 1/2X-Y-chains in a magnetic field. For special values of the parameters we solve the equation of motion for…