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Physics Letters A

Possible first order phase transition in the one-dimensional helical Hubbard model

Wenzheng Wang, Shi‐Jie Xiong

Published Jul 1, 1991• 6 citations
Publisher
DOI
10.1016/0375-9601(91)90719-o

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A Z N -symmetric theory with four-spin interactions on a three-dimensional FCC lattice is analysed. The model possesses an unusual semi-local symmetry and is self-dual. For N<N c approximately=5 it undergoes a single, first-order transition, whereas for N>or=N c it exhibits two continuous transitions which may or may not be infinite order. The intermediate phase appearing between the ferromagnetic ordered and disordered phases for N>or=N c is a massless phase with no long-range order. The behaviour of the theory is strongly reminiscent of that of the two-dimensional Z N spin models and the four-dimensional Z N gauge theories and, quite naturally, constitutes a three-dimensional interpolating model. The possible relevance of this and related models to the Lifshitz point problem in certain helical magnetic and liquid crystal systems is briefly discussed.

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Recent progress in experiments on trapped ultracold atoms has made it possible to study the interplay between magnetism and superfluid-insulator transitions in the boson Hubbard model. We report on quantum Monte Carlo simulations of the spin-1 boson Hubbard model in the ground state. For antiferromagnetic interactions favoring singlets, we present exact numerical evidence that the superfluid-insulator transition is first (second) order for even (odd) Mott lobes. Inside even lobes, we search for nematic-to-singlet first order transitions. In the ferromagnetic case where transitions are all continuous, we map the phase diagram and show the superfluid to be ferromagnetic. We compare the quantum Monte Carlo phase diagram with a third order perturbation calculation.
We study the spin-1/2 and spin-1 [Formula: see text] Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing [Formula: see text] bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with [Formula: see text] bonds along parallel chains and with J1 bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 [Formula: see text] model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κc1 = 0.80 ± 0.01, and a second critical point at κc2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κc1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.
A Z N -symmetric theory with four-spin interactions on a three-dimensional FCC lattice is analysed. The model possesses an unusual semi-local symmetry and is self-dual. For N<N c approximately=5 it undergoes a single, first-order transition, whereas for N>or=N c it exhibits two continuous transitions which may or may not be infinite order. The intermediate phase appearing between the ferromagnetic ordered and disordered phases for N>or=N c is a massless phase with no long-range order. The behaviour of the theory is strongly reminiscent of that of the two-dimensional Z N spin models and the four-dimensional Z N gauge theories and, quite naturally, constitutes a three-dimensional interpolating model. The possible relevance of this and related models to the Lifshitz point problem in certain helical magnetic and liquid crystal systems is briefly discussed.