Antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

Abstract

We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx and uniform longitudinal field hz. Using the density matrix renormalization group calculation combined with a finite-size scaling the ground state phase diagram in (hx, hz) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in hz the scaling behavior of the mass gap in the vicinity of the critical point (hx = 1/2, hz = 0) is established. It is found that the form of the transition line near the classical multicritical point (hx = 0, hz = 1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

Quantum and Thermal Fluctuations in the Ising Chains: A Case Study of Spin-Two System

“…Among the various systems, one dimensional (1D) and quasi-one dimensional systems are fantastic playground for quantum phase transitions (QPTs), with rather unique properties [3,5,6,8,10,11,12]. There are various reasons for this special behaviour.…”

“…The transition describes an abrupt change in the ground state of a many-body system due to its quantum fluctuations. At the critical point where the quantum phase transition (QPT) occurs, the ground state of the system undergoes a qualitative change in some of its properties [5,6]. QPT can be described as second order phase transition.…”

“…The study of the field-induced effects in low-dimensional quantum spin systems has been attracting much interest from theoretical and experimental points of view [1,3,5,6,8,11]. For example, the behaviour of the one-dimensional antiferromagnetic XXZ model in a transverse magnetic field is drastically different in comparison with the case of the longitudinal field [8, 21, and 22].…”

“…In Physics, a quantum phase transition (QPT) is a phase transition between different quantum phases of matter at absolute zero temperature [1][2][3][4][5][6][7][8]. Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physical parameter such as magnetic field or pressure at absolute zero temperature.…”

Gap exponent of theXXZmodel in a transverse field

“…The applicability of the mean-field approximation has been studied by comparing with the DMRG results of magnetization and structure factor 15 . Recently the effect of longitudinal magnetic field on both the Ising model in Transverse Field (TF) 16 and the XXZ model in TF has been discussed 17 .…”