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arXiv:quant-ph/0701028

First order quantum phase transitions in the XX spin chain

Feng Pan, Nan Ma, Xin Guan, J. P. Draayer

Published Jan 8, 2007• 0 citations
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Abstract

Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitions are of the first order due to the level-crossing. The ground state in the thermodynamic limit will be divided into three distinguishable quantum phases.

DOI
10.48550/arxiv.quant-ph/0701028

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Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitions are of the first order due to the level-crossing. The ground state in the thermodynamic limit will be divided into three distinguishable quantum phases.
A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed, which can easily be used to study general spin-1/2 interaction systems. As an example, The code is applied to study XXX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field. It shows that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitional behavior in the ground state of the system in the thermodynamic limit is also studied.
The ground state of a one-dimensional spin-1/2 chain with periodical boundary condition in the Heisenberg XY model is investigated. We consider the spatial correlation and concurrence between any nearest-neighbor pair of spins under the conditions of different coupling strength, anisotropic parameter and magnitude of a transverse field. Quantum phase transitions due to the competition between coupling and alignment which cause the abrupt changes of the correlation and concurrence are observed. The transition are direct results of the level crossing.
We present exact results for the ground-state and thermodynamic properties of the spin-1/2 XX\mathit{XX}XX chain with three-site interactions in a random (Lorentzian) transverse field. We discuss the influence of randomness on the quantum critical behavior known to be present in the nonrandom model. We find that at zero temperature the characteristic features of the quantum phase transition, such as kinks in the magnetization versus field curve, are smeared out by randomness. However, at low but finite temperatures signatures of the quantum critical behavior are preserved if the randomness is not too large. Even the quantum critical region may be slightly enlarged for very weak randomness. In addition to the exact results for Lorentzian randomness we present a more general discussion of an arbitrarily random transverse magnetic field based on the inspection of the moments of the density of states.
Abstract A spin‐½ XX chain with three‐spin and uniform long‐range interactions among the z components of the spins is constructed. Based upon the model, using the Jordan–Wigner transformation, the thermodynamic quantities and spin transports of the system are evaluated exactly. The phase diagram together with the key parameters characterizing quantum phase transitions is presented. It is noted that, similarly to classical first‐order phase transitions, there are also the metastable states “supercooled” and “superheated” in the first‐order quantum phase transitions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The ground-state entanglement in a transverse spin-1/2 XX chain with a magnetization current is studied. By introducing a magnetization current to the system, a quantum phase transition to current-carrying phase may be presented with the variation of the driving field λ for the magnetic field h > 1; and the ground-state entanglement arises simultaneously at the critical point of quantum phase transition. In our model, the introduction of magnetization current may result in more entanglement between any two nearest-neighbour spins.
We study quantum spin models with nearest- and next-nearest-neighbor exchange interactions by means of exact solutions. Depending on the representation, the models can also be viewed as spin ladders with interchain couplings and with ring biquadratic spin-spin interactions. The ground-state phase diagram is constructed as a function of the next-nearest-neighbor couplings and an external magnetic field. Several quantum phase transitions in the ground state, including the possibility of a first-order quantum phase transition, governed by the external magnetic field, are predicted. The low-energy conformal behavior of the low-lying excitations is studied in the commensurate and incommensurate phases. Finally, the properties of the models at finite temperature are studied exactly. A finite set of nonlinear integral equations determining the thermodynamic potential at arbitrary temperature and external magnetic field is derived and solved in several important cases. The results for the magnetic susceptibility and the Sommerfeld coefficient of the specific heat are presented.