We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two pinning potential terms of dual fields that stabilize competing orders and allows different types of quantum phase transition to happen between two ordered phases. At the transition point, elementary excitations change from the topological soliton of one of the dual fields to that of the other, thus it can be characterized as a topological transition. We compute the dynamical susceptibilities and the entanglement entropy, which gives us access to the central charge, of the system using a numerical technique of infinite time-evolving block decimation and characterize the universality class of the transition as well as the nature of the order in each phase. The possible realizations of such transitions in experimental systems both for condensed matter and cold atomic gases are also discussed.
We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of
N copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of
N order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO(
N)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of
N. For
N=2 and
N=3, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for
N≥4, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO(
N) symmetry, including spin-
1/2 and spin-
1 two-leg ladders, that realize a direct transition between an SO(
N) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.
We show that all so(N)_{1} universality class quantum criticalities emerge when one-dimensional generalized cluster models are perturbed with Ising or Zeeman terms. Each critical point is described by a low-energy theory of N linearly dispersing fermions, whose spectrum we show to precisely match the prediction by so(N)_{1} conformal field theory. Furthermore, by an explicit construction we show that all the cluster models are dual to nonlocally coupled transverse field Ising chains, with the universality of the so(N)_{1} criticality manifesting itself as N of these chains becoming critical. This duality also reveals that the symmetry protection of cluster models arises from the underlying Ising symmetries and it enables the identification of local representations for the primary fields of the so(N)_{1} conformal field theories. For the simplest and experimentally most realistic case that corresponds to the original one-dimensional cluster model with local three-spin interactions, our results show that the su(2)_{2}≃so(3)_{1} Wess-Zumino-Witten model can emerge in a local, translationally invariant, and Jordan-Wigner solvable spin-1/2 model.
The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled one-dimensional cold atomic gases. The weak interactions within the atomic clouds provide a sine-Gordon realization in the semiclassical regime. Furthermore, the intricate microscopic dynamics prevents a quantitative understanding of the effective sine-Gordon validity realm. In this work, we focus on a spin-ladder realization and observe the emergent sine-Gordon dynamics deep in the quantum regime. We use matrix-product state techniques to numerically characterize the low-energy sector of the system and compare it with the exact field-theory predictions. From this comparison, we obtain quantitative boundaries for the validity of the sine-Gordon description. We provide encompassing evidence for the emergent field theory by probing its rich spectrum and by observing the signatures of integrable dynamics in scattering events.
Investigation of strongly interacting, nonlinear quantum field theories (QFTs) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFTs using mesoscopic superconducting circuit lattices. Using the Josephson effect as the source of nonlinear interaction, we investigate generalizations of the quantum sine-Gordon model. In particular, we consider a two-field generalization, the double sine-Gordon model. In contrast to the sine-Gordon model, this model can be purely quantum integrable, when it does not admit a semiclassical description---a property that is generic to many multifield QFTs. The primary goal of this work is to investigate different thermodynamic properties of the double sine-Gordon model and propose experiments that can capture its subtle quantum integrability. First, we analytically compute the mass spectrum and the ground-state energy in the presence of an external ``magnetic'' field using Bethe ansatz and conformal perturbation theory. Second, we calculate the thermodynamic Bethe ansatz equations for the model and analyze its finite temperature properties. Third, we propose experiments to verify the theoretical predictions.
Motivated by the realization of coupled Luttinger liquids in a split condensate for quantum sine-Gordon (SG) model [Haller et al., Nature 466, 597 (2010); Schweiglet et al., Nature 545, 323 (2017); Nat. Phys. 17, 559 (2021)], here we study the phase transition in coupled condensates using the bosonization method. We show that when these condensates have different velocities
ui and Luttinger parameters
Ki, the physics is described by a generalized SG model, which is also exactly solvable. We use various approaches, including the Wilson renormalization group, correlation function, variational wave function, and the equivalent Coulomb gas methods, demonstrating the phase transition at
2=1/(4K1)+1/(4K2). The physical meaning of this boundary is explained by the density-phase uncertainty principle, showing how the many-body interactions drive the coupled condensates from two gapless phases to one gapless phase. The relative phase between the condensates may fundamentally affect the band structure, yet it will not affect this boundary. Furthermore, we also discuss the relevance of our result in the two-dimensional models for the Berezinskii-Kosterlitz-Thouless transition, from which the physical meaning of this boundary is self-evident. Our results can be used to study the phase transitions in one-dimensional coupled models with Fermions and Bosons, and even the Kane-Fisher model with impurities, and study their phase transitions, non-Gaussian dynamics, and thermalization, which may be of great interest in quantum simulation.