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arXiv:1904.11398 · Journal of Physics Condensed Matter

Universality of Heisenberg–Ising chain in external fields

Haiyuan Zou, Rong Yu, Jianda Wu

Published Oct 9, 2019• 8 citations
arXivHTMLPDF

Abstract

Abstract Motivated by the recent surge of transverse-field experiments on quasi-one-dimensional (1D) antiferromagnets Sr(Ba)Co 2 V 2 O 8 , we investigate the quantum phase transition (QPT) in a Heisenberg–Ising chain under a combination of two in-plane inter-perpendicular transverse fields and a four-period longitudinal field, where the in-plane transverse field is either uniform or staggered. We show that the model can be unitary mapped to the 1D transverse-field Ising model (1DTFIM) when the x and y components of the spin interaction and the four-period field are absent. When these two terms are present, following both analytical and numerical efforts, we demonstrate that the system undergoes a second-order QPT with increasing transverse fields, where the critical exponents as well as the central charge fall into the universality of 1DTFIM. Our results naturally identify the 1DTFIM universality of 1D quantum phase transitions observed in the existed experiments in Sr(Ba)Co 2 V 2 O 8 with transverse field applied along either [ ] or [ ] direction. Upon varying the tuning parameters, a critical surface with 1DTFIM universality is determined and silhouetted to exhibit the general presence of the universality in a much wider scope of models than conventional understanding. Our results provide a broad guiding framework to facilitate the experimental realization of 1DTFIM universality in real materials.

DOI
10.1088/1361-648x/ab4c71

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Abstract Motivated by the recent surge of transverse-field experiments on quasi-one-dimensional (1D) antiferromagnets Sr(Ba)Co 2 V 2 O 8 , we investigate the quantum phase transition (QPT) in a Heisenberg–Ising chain under a combination of two in-plane inter-perpendicular transverse fields and a four-period longitudinal field, where the in-plane transverse field is either uniform or staggered. We show that the model can be unitary mapped to the 1D transverse-field Ising model (1DTFIM) when the x and y components of the spin interaction and the four-period field are absent. When these two terms are present, following both analytical and numerical efforts, we demonstrate that the system undergoes a second-order QPT with increasing transverse fields, where the critical exponents as well as the central charge fall into the universality of 1DTFIM. Our results naturally identify the 1DTFIM universality of 1D quantum phase transitions observed in the existed experiments in Sr(Ba)Co 2 V 2 O 8 with transverse field applied along either [ ] or [ ] direction. Upon varying the tuning parameters, a critical surface with 1DTFIM universality is determined and silhouetted to exhibit the general presence of the universality in a much wider scope of models than conventional understanding. Our results provide a broad guiding framework to facilitate the experimental realization of 1DTFIM universality in real materials.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudospin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudospin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse-field only emerges at zero field and is of the second order. Several critical exponents obtained by finite-size scaling analysis are the same as those in the 1D transverse-field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.
We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx{h}_{x}hx​ and uniform longitudinal field hz.{h}_{z}.hz​. Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in (hx,hz){(h}_{x}{,h}_{z})(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{h}_{z}hz​ the scaling behavior of the mass gap in the vicinity of the critical point (hx=1/2,hz=0){(h}_{x}{=1/2,h}_{z}=0)(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){(h}_{x}{=0,h}_{z}=1)(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.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis are the same as those in the 1D transverse field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.
We report ^{51}V NMR and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo_{2}V_{2}O_{8} under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the Néel temperatures unveils a 1D quantum critical point (QCP) at H_{c}^{1D}≈4.7 T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at H_{c}^{1D} is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional E_{8} Lie algebra. These excitations are nondiffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive E_{8} phase in the compound, and open a new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group, and the density matrix renormalization group methods. It is found that in the magnetic field--bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau, and spin-polarized phases are identified in a longitudinal field, while in a transverse field there are five phases including singlet dimer, Haldane, Z2{Z}_{2}Z2​ symmetry breaking, quasi-1/2 magnetization plateau, and quasi-spin-polarized phases. A reentrant behavior of the staggered magnetization in a transverse field is observed. The quantum critical behaviors in longitudinal and transverse magnetic fields are disclosed to fall into different universality classes with corresponding conformal field central charge c=1c=1c=1 and 1/21/21/2, respectively. The experimental data of the compound NTENP under both longitudinal and transverse magnetic fields are nicely fitted, and the Luttinger liquid behavior of low-temperature specific heat experimentally observed is also confirmed.
For a system at absolute zero temperature, all thermal fluctuations are frozen out, while quantum fluctuations prevail.These microscopic quantum fluctuations can induce a quantum phase transition (QPT) in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value.This paper presents a detailed and quantitative study of the magnetic properties of Ising two-spin system at zero temperature in the presence of longitudinal, transverse and mixed fields, and also at finite temperatures.At the critical longitudinal magnetic field, the system is found to undergo a QPT to a ferromagnetic state.For this system, an infinitesimal departure from zero transverse field is found to trigger off QPT and also remove the degeneracies that persisted even in the presence of longitudinal field.These quantum fluctuations, leading to QPT are more evident in the mixed field than the separate effect of longitudinal and transverse fields.The observed quantum effects at zero temperature for this system are found to be completely wiped out at finite temperatures due to thermal fluctuations.A temperature increase favours antiferromagnetic alignment of spins, while a decrease in temperature favours ferromagnetic alignment.