Bayesian critical points in classical lattice models

• URL: http://arxiv.org/abs/2504.01264v1
• Date: Wed, 02 Apr 2025 00:25:27 GMT
• Title: Bayesian critical points in classical lattice models
• Authors: Adam Nahum, Jesper Lykke Jacobsen,
• Abstract summary: Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian.<n>We examine the resulting "conditioned derivation ensembles", finding that they show many new phase transitions and new renormalization-group fixed points.<n>We make connections with quantum dynamics, in particular with "charge sharpening" in 1D, by giving a formalism for measurement of classical processes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from measurement, our knowledge is updated according to Bayes' theorem. We examine the resulting "conditioned ensembles", finding that they show many new phase transitions and new renormalization-group fixed points. (Similar conditioned ensembles also describe "partial quenches" in which some of the system's degrees of freedom are instantaneously frozen, while the others continue to evolve.) After describing general features of the replica field theories for these problems, we analyze the effect of measurement on illustrative critical systems, including: critical Ising and Potts models, which show surprisingly rich phase diagrams, with RG fixed points at weak, intermediate, and infinite measurement strength; various models involving free fields, XY spins, or flux lines in 2D or 3D; and geometrical models such as polymers or clusters. We make connections with quantum dynamics, in particular with "charge sharpening" in 1D, by giving a formalism for measurement of classical stochastic processes: e.g. we give a purely hydrodynamic derivation of the known effective field theory for charge sharpening. We discuss qualitative differences between RG flows for the above measured systems, described by $N\to 1$ replica limits, and those for disordered systems, described by $N\to 0$ limits. In addition to discussing measurement of critical states, we give a unifying treatment of a family of inference problems for non-critical states. These are related to the Nishimori line in the phase diagram of the random-bond Ising model, and are relevant to various quantum error correction problems. We describe distinct physical interpretations of conditioned ensembles and note interesting open questions.

Related papers

• Measurement-induced phase transitions in quantum inference problems and quantum hidden Markov models [0.0]
  We show a connection between'sharpening' and 'learnability' order parameters and quantum hidden Markov models. We study the Haar-random U(1)-symmetric monitored quantum circuit and tree, mapping each to inference models that we call the planted SSEP and planted XOR. We present an exact solution of the entire phase boundary, which displays re-entrance as does the 2D RBIM.
  arXiv  Detail & Related papers  (2025-04-11T18:00:06Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Oddities in the Entanglement Scaling of the Quantum Six-Vertex Model [0.0]
  We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder. We show a novel logarithmic correction to the expected entanglement scaling when the system size is odd. Our findings highlight the crucial role of system size parity in determining the entanglement properties of this model.
  arXiv  Detail & Related papers  (2025-02-26T14:09:40Z)
• Decoherence-induced self-dual criticality in topological states of matter [0.9961452710097684]
  We show that measurement-induced phase transitions can be viewed as decoherence-induced mixed states.<n>Integrating these connections we investigate the role of self-dual symmetry in mixed states.<n>Our results point to a way towards a general understanding of mixed-state criticality in open quantum systems.
  arXiv  Detail & Related papers  (2025-02-19T19:00:02Z)
• CWF: Consolidating Weak Features in High-quality Mesh Simplification [50.634070540791555]
  We propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term.
  arXiv  Detail & Related papers  (2024-04-24T05:37:17Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• 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)
• Frustration shapes multi-channel Kondo physics: a star graph perspective [0.31317409221921144]
  We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties.
  arXiv  Detail & Related papers  (2022-05-02T10:21:24Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
  Quantum scars are non-thermal eigenstates characterized by low entanglement entropy. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
  arXiv  Detail & Related papers  (2020-11-16T19:05:50Z)
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States [0.0]
  We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems. Under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential.
  arXiv  Detail & Related papers  (2020-10-29T03:24:19Z)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.