In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one dimension. The low-temperature phase is characterized by a quantum bright soliton without long range order; the high-temperature phase is a free gas. Numerical calculations for finite particle numbers show a specific heat scaling as $N^2$ , consistent with a vanishing transition region in the thermodynamic limit.In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one dimension. The low-temperature phase is characterized by a quantum bright soliton without long range order; the high-temperature phase is a free gas. Numerical calculations for finite particle numbers show a specific heat scaling as $N^2$, consistent with a vanishing transition region in the thermodynamic limit.

arXiv:1610.09070Oct 28, 20162 citations

First-order phase transition in an approximately one-dimensional system

V. N. Bogomolov, E.V. Kolla, Yu. A. Kumzerov

ZhETF Pisma RedaktsiiuJan 1, 19853 citations

Effects of quenched disorder on spin-1/2 quantumXXZchains

Curtis A. Doty, Daniel S. Fisher

We analyze the zero-temperature phase diagram of the spin-1/2 quantum XXZ chain in the presence of weak disorder. The effects of various random perturbations are considered, including random fields and random exchange. For random perturbations that preserve the XY symmetry, we find a phase transition, as the anisotropy parameter is varied, from a ground state with quasi-long-range order (as in the pure system) to one in which typical correlation functions decay rapidly. The critical behavior at this transition is shown to be in the universality class of the Giamarchi-Schulz transition for one-dimensional bosons in a random potential. Random perturbations that break the XY symmetry are found always to destroy the quasi-long-range order of the ground state. Properties of the resulting random phases are also discussed.We analyze the zero-temperature phase diagram of the spin-1/2 quantum XXZ chain in the presence of weak disorder. The effects of various random perturbations are considered, including random fields and random exchange. For random perturbations that preserve the XY symmetry, we find a phase transition, as the anisotropy parameter is varied, from a ground state with quasi-long-range order (as in the pure system) to one in which typical correlation functions decay rapidly. The critical behavior at this transition is shown to be in the universality class of the Giamarchi-Schulz transition for one-dimensional bosons in a random potential. Random perturbations that break the XY symmetry are found always to destroy the quasi-long-range order of the ground state. Properties of the resulting random phases are also discussed.

Physical review. B, Condensed matterFeb 1, 1992123 citations

First-Order Phase Transitions in One-Dimensional Steady States

Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg

arXiv:cond-mat/9706114Journal of Statistical PhysicsFeb 1, 199860 citations

PHASE TRANSITIONS IN SMALL AND LONG-RANGE INTERACTING SYSTEMS.

Yaroslav Ispolatov

Jan 1, 20020 citations

N^2

, consistent with a vanishing transition region in the thermodynamic limit.