2016/02/02 by H. Wilming, Henrik Wilming, Michael J. Kastoryano +5
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Continuous symmetry #Detailed balance #Dissipative system #Explicit symmetry breaking #Lattice (music) #Local symmetry #Physics #Quantum #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum fluctuation #Quantum many-body systems #Quantum mechanics #Spontaneous symmetry breaking #Stationary state #Statistical physics #Symmetry breaking #Thermodynamic limit #cond-mat.other #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4978328
published as J. Math. Phys. 58, 033302 (2017) · 15 pages
arxiv created 2016/02/02 · openalex publication_date 2017/03/01 · arxiv updated 2017/04/05 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.