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arXiv:2503.09437

Dimension-raising phase transitions in driven magnets and condensates

Zhizhen Chen, Zi Cai

Published Mar 12, 2025• 0 citations
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Abstract

We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers, between phases with various dimensions. We study an interacting rotor model whose instantaneous Hamiltonian keeps the one-dimensional (1D) feature at any given time. Despite this, an emergent two-dimensional (2D) phase appears when the driving frequency exceeds a critical value, at which a dimension-raising phase transition takes place. We find that the nonequilibrium feature of the system could qualitatively change the finite temperature critical behavior of the emergent 2D phase and make it different from its equilibrium counterpart. A four-dimensional (4D) generalization and experimental realizations of the proposed model based on a programmable reconfiguration technique in optical tweezers setups have also been discussed.

DOI
10.48550/arxiv.2503.09437

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We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers, between phases with various dimensions. We study an interacting rotor model whose instantaneous Hamiltonian keeps the one-dimensional (1D) feature at any given time. Despite this, an emergent two-dimensional (2D) phase appears when the driving frequency exceeds a critical value, at which a dimension-raising phase transition takes place. We find that the nonequilibrium feature of the system could qualitatively change the finite temperature critical behavior of the emergent 2D phase and make it different from its equilibrium counterpart. A four-dimensional (4D) generalization and experimental realizations of the proposed model based on a programmable reconfiguration technique in optical tweezers setups have also been discussed.
Abstract We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers, between phases with various dimensions. We study an interacting rotor model whose instantaneous Hamiltonian keeps the one-dimensional feature at any given time. Despite this, an emergent two-dimensional (2D) phase appears when the driving frequency exceeds a critical value, at which a dimension-raising phase transition takes place. We find that the nonequilibrium feature of the system could qualitatively change the finite temperature critical behavior of the emergent 2D phase and make it different from its equilibrium counterpart. A four-dimensional generalization and experimental realizations of the proposed model based on a programmable reconfiguration technique in optical tweezers setups have also been discussed.
A deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential both to advance our fundamental physics understanding and to harness technological opportunities arising from optically controlled quantum many-body states. This paper provides a numerical study of dynamical phases and the transitions between them in the nonequilibrium steady state of the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. We demonstrate a nonthermal transition that is characterized by a qualitative change in the magnon distribution from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive. A finite-size analysis reveals static and dynamical critical scaling at the transition, with a discontinuous slope of the magnon number versus driving field strength and critical slowing down at the transition point. Implications for experiments on quantum materials and polariton condensates are discussed.
Understanding how a system's behavior extrapolates beyond 3D is a fundamental question in physics, spanning topics from unification theories to critical phenomena. In statistical physics, fluctuations' strength is highly sensitive to dimensionality, affecting phase transitions. In low dimensions, phase transitions are suppressed, while high-dimensional systems exhibit simpler mean-field behavior. In some cases, like the Anderson localization-delocalization transition in disordered media, criticality remains non-trivial even in dimensions larger than three, presenting challenges to existing frameworks. In this work, using a periodically-driven ultracold atomic gas to engineer disorder and synthetic dimensions, we experimentally observe a phase transition between localized and delocalized phases. The results display three key features of the 4D transition: 1) observables follow d=4 critical scale invariance, 2) critical exponents match numerical predictions for the 4D Anderson transition, and 3) they agree with Wegner's relation in 4D. These findings provide a new avenue for exploring complex critical phenomena in higher dimensions.
The study of phases is useful for understanding novel states of matter. One such state of matter is time crystals which constitute periodically driven interacting many-body systems that spontaneously break time translation symmetry. Time crystals with arbitrary periods (and dimensions) can be realized using the model of Bose-Einstein condensates bouncing on periodically driven mirror(s). In this work, we identify the different phases that characterize the two-dimensional time crystal. By determining the optimal initial conditions and value of system parameters, we provide a practical route to realize a specific phase of the time crystal. These different phases can be mapped to the many-body states existing on a two-dimensional Hubbard lattice model, thereby opening up interesting opportunities for quantum simulation of many-body physics in time lattices.
We present a comprehensive theoretical framework to explore emergent quantum phases in two-dimensional (2D) materials driven by nonlocal three-body interactions. By formulating a generalized Hamiltonian with nonlocal exchange terms, we derive analytical expressions for the energy gap, wave functions, and critical phase transitions. Our model predicts a topological phase transition at critical interaction strengths, validated through extensive numerical simulations. We analyze the robustness of these phases against temperature, disorder, and external fields, offering insights into their stability and tunability. These findings advance our understanding of quantum phases in 2D systems, with potential applications in quantum computing and spintronics.
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.