Chinese Physics B

Ferromagnetic Heisenberg spin chain in a resonator

Yusong Cao, Junpeng Cao, Heng Fan

Published Jul 12, 2021• 0 citations

Abstract

We investigate the properties of a generalized Rabi model by replacing the two-level atom in Rabi model with a ferromagnetic Heisenberg spin chain. We find that the dynamical behavior of the system can be divided into four categories. The energy spectrum of the ground state and some low excited states are obtained. When the magnons and the photon are in resonance, the model is exactly solvable and the rigorous solution is obtained. Near the resonance point where the detuning is small, the system is studied with the help of perturbation theory. This model has a spontaneously breaking of parity symmetry, suggesting the existence of a quantum phase transition. The critical exponent from the normal phase is computed.

DOI: 10.1088/1674-1056/ac1334

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Chinese Physics B

Ferromagnetic Heisenberg spin chain in a resonator

Yusong Cao, Junpeng Cao, Heng Fan

Published Jul 12, 2021• 0 citations

Publisher

Abstract

DOI: 10.1088/1674-1056/ac1334

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T

. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.

We study the zero-temperature properties of a spin-

1/2

Heisenberg chain with an additional three-site chiral term of strength

g

. The model is known to be integrable and previous work using Bethe ansatz has identified a phase transition from the usual critical state for

g< g_c = 2/π

to a chiral phase for

g>g_c

. Here we combine analytical and computational approaches to demonstrate that the transition point comprises an unusual Lifshitz transition with dynamical critical exponent

z=3

, and the chiral phase is a partially spin-polarized phase which spontaneously breaks SU(2) symmetry. We derive a strongly interacting chiral boson field theory for the critical point, and show that even its small-momentum, low-energy response is non-trivial. We also determine the universal properties of the chiral phase, and specifically show that it has a simultaneous quadratically dispersing ferromagnetic "magnon" mode coexisting with the power-law singularities and linearly dispersing excitations typical of a Luttinger liquid. Our conclusions are validated using numerics based on matrix product state methods and exact diagonalization.

The excitation spectrum of the ferromagnetic

s=\frac{1}{2}

Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with

s>\frac{1}{2}

, such as CsNi

{\mathrm{F}}_{3}

, and on the soliton aspect of the classically treated systems.

The properties of the ferromagnetic frustrated spin-

S

one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for

s=1∕2

are sufficiently strong to change the classical critical exponents, while for spin systems with $s\ensuremath{\geqslant}1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.