Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models

• URL: http://arxiv.org/abs/2603.18285v1
• Date: Wed, 18 Mar 2026 21:16:22 GMT
• Title: Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models
• Abstract summary: We present a systematic framework for analyzing continuous symmetries in fermionic systems.<n>We identify the structure of this Lie algebra using the theory of semisimple Lie algebras.<n>We classify these order parameters according to the symmetries they break.
• Score: 2.8110777003480654
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. (Abridged. Please see the PDF manuscript for the complete abstract and specific model applications.)

Related papers

• SIM-GRAPH: A universal guide to symmetric interactions [0.0]
  In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries.<n>We present the SIM-GRAPH method, which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems.
  arXiv  Detail & Related papers  (2026-09-09T10:20:58Z)
• Generalized symmetries, invariant solutions and conservation laws in the Jaynes-Cummings model [41.99844472131922]
  We investigate the Jaynes--Cummings model (JCM) using Lie symmetry analysis and conservation-law theory.<n>The dynamics is formulated as a system of partial differential equations by projecting the von Neumann equation onto the atomic degrees of freedom.<n>We derive additional conserved currents involving atomic populations, coherence, reduced-state purity, and moments of the field characteristic function.
  arXiv  Detail & Related papers  (2026-06-14T01:42:11Z)
• Entanglement Asymmetry for Higher and Noninvertible Symmetries [0.13048920509133807]
  Entanglement asymmetry is an observable in quantum systems.<n>In this paper we define the asymmetry for generalized finite symmetries.<n>We study in detail applications to (1+1)-dimensional theories.
  arXiv  Detail & Related papers  (2025-09-19T18:00:01Z)
• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model [44.99833362998488]
  We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory.<n>Exploiting Lie symmetries in conjunction with the model's Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations.<n>Our approach yields a unified framework for interpreting and stabilising higher time-derivative dynamics.
  arXiv  Detail & Related papers  (2025-05-09T15:16:40Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Computing Game Symmetries and Equilibria That Respect Them [77.72705755558839]
  We study the computational of identifying and using symmetries in games.<n>We find a strong connection between game symmetries and graph automorphisms.<n>We show that finding a Nash equilibrium that respects a given set of symmetries is exactly as hard as Brouwer fixed point and gradient descent problems.
  arXiv  Detail & Related papers  (2025-01-15T16:15:16Z)
• 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)
• Latent Space Symmetry Discovery [31.28537696897416]
  We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions. We show that our model can express nonlinear symmetries under some conditions about the group action. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
  arXiv  Detail & Related papers  (2023-09-29T19:33:01Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis [38.92081817503126]
  We study discrete morphological symmetries of dynamical systems. These symmetries arise from the presence of one or more planes/axis of symmetry in the system's morphology. We exploit these symmetries using data augmentation and $G$-equivariant neural networks.
  arXiv  Detail & Related papers  (2023-02-21T04:10:16Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Classifying phases protected by matrix product operator symmetries using matrix product states [0.0]
  We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:25:30Z)
• String order parameters for symmetry fractionalization in an enriched toric code [0.0]
  We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures are robust under the effects of external fields and interactions.
  arXiv  Detail & Related papers  (2020-11-05T17:15:53Z)
• Quantifying Algebraic Asymmetry of Hamiltonian Systems [0.0]
  We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. The asymmetry of the $q$-deformed integrable spin chain models is calculated.
  arXiv  Detail & Related papers  (2020-01-08T08:12:20Z)

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.