Quantum criticality in open quantum systems from the purification perspective

• URL: http://arxiv.org/abs/2602.21979v1
• Date: Wed, 25 Feb 2026 14:57:44 GMT
• Title: Quantum criticality in open quantum systems from the purification perspective
• Authors: Yuchen Guo, Shuo Yang,
• Abstract summary: Open quantum systems host mixed-state phases that go beyond the symmetry-protected topological and spontaneous symmetry-breaking paradigms.<n>We develop a purification-based framework that characterizes all mixed-state phases in one-dimensional systems.<n>We find a rich phase structure, including pyramid symmetry-breaking regions and a fully symmetry-broken phase at the cube center.
• Score: 16.364682124857485
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Open quantum systems host mixed-state phases that go beyond the symmetry-protected topological and spontaneous symmetry-breaking paradigms established for closed, pure-state systems. Developing a unified and physically transparent classification of such phases remains a central challenge. In this work, we introduce a purification-based framework that systematically characterizes all mixed-state phases in one-dimensional systems with $\mathbb{Z}_2^σ \times \mathbb{Z}_2^τ$ symmetry. By introducing an ancillary $κ$ chain and employing decorated domain-wall constructions, we derive eight purified fixed-point Hamiltonians labeled by topological indices $(μ_{στ},μ_{τκ},μ_{κσ}) \in \{\pm1\}^3$. Tracing out the ancilla recovers the full structure of mixed-state phases, including symmetric, strong-to-weak spontaneous symmetry breaking, average symmetry-protected topological phases, and their nontrivial combinations. Interpolations between the eight fixed points naturally define a three-dimensional phase diagram with a cube geometry. The edges correspond to elementary transitions associated with single topological indices, while the faces host intermediate phases arising from competing domain-wall decorations. Along the edges, we identify a class of critical behavior that connects distinct strong-to-weak symmetry-breaking patterns associated with distinct strong subgroups, highlighting a mechanism unique to mixed-state settings. Large-scale tensor-network simulations reveal a rich phase structure, including pyramid-shaped symmetry-breaking regions and a fully symmetry-broken phase at the cube center. Overall, our purification approach provides a geometrically transparent and physically complete classification of mixed-state phases, unified with a single $\mathbb{Z}_2^σ \times \mathbb{Z}_2^τ \times \mathbb{Z}_2^κ$ model.

Related papers

• Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States [41.99844472131922]
  We develop a rigorous theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states.<n>We also construct $$-spectra of a class of invertible states and quantum cellular automata, which allows us to classify both anomalies and symmetry protected topological phases up to blend equivalence.
  arXiv  Detail & Related papers  (2025-12-01T19:00:01Z)
• Subdimensional entanglement entropy: from virtual response to mixed-state holography [13.658615899723381]
  We introduce the textitsubdimensional entanglement entropy (SEE) as a response theory characterizing many-body systems.<n>By bridging entanglement, mixed-state and categorical symmetries, holographic principles of topological order, and geometric-topological responses, SEE provides a unified framework.
  arXiv  Detail & Related papers  (2025-10-17T15:54:55Z)
• Topological Holography for Mixed-State Phases and Phase Transitions [5.6658173165064785]
  We extend the symmetry topological field theory (SymTFT) framework to open quantum systems.<n>We study (1+1)-dimensional mixed-state phases through condensable algebras in the SymTFT.<n>We show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.
  arXiv  Detail & Related papers  (2025-07-08T17:51:00Z)
• Topological Phase Transitions and Mixed State Order in a Hubbard Quantum Simulator [36.556659404501914]
  Topological phase transitions challenge conventional paradigms in many-body physics.<n>We observe such a transition between one-dimensional crystalline symmetry-protected topological phases.<n>Our results demonstrate how topology and information influence quantum phase transitions.
  arXiv  Detail & Related papers  (2025-05-22T17:58:35Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems.<n>How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order [17.38734393793605]
  We propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders.<n>This new phase is absent from prior studies and cannot exist in conventional closed systems.
  arXiv  Detail & Related papers  (2024-10-17T16:36:53Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup [0.6675805308519986]
  Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study an emergent $mathbbZ$-gauged system with global $U(1)$. We also discuss the stability of these phases and the critical points to small perturbations and their potential experimental realizations.
  arXiv  Detail & Related papers  (2024-01-22T05:46:49Z)
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic [11.002608494115886]
  Topological phases in mixed quantum states, originating from textitdecoherence in open quantum systems, have recently garnered significant interest.<n>We present a systematic classification and characterization of average symmetry-protected topological phases.<n>We also formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems.
  arXiv  Detail & Related papers  (2023-05-25T18:04:22Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.