Symmetry shapes thermodynamics of macroscopic quantum systems

• URL: http://arxiv.org/abs/2402.04214v1
• Date: Tue, 6 Feb 2024 18:13:18 GMT
• Title: Symmetry shapes thermodynamics of macroscopic quantum systems
• Authors: Vasco Cavina, Ariane Soret, Timur Aslyamov, Krzysztof Ptaszy\'nski, Massimiliano Esposito
• Abstract summary: We show that the entropy of a system can be described in terms of group-theoretical quantities. We apply our technique to generic $N$ identical interacting $d$-level quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\boldsymbol{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group $\text{S}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\boldsymbol{x})=e(\boldsymbol{x})-\beta^{-1}s(\boldsymbol{x})$, where $e(\boldsymbol{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.

Related papers

• A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality [0.0]
  We introduce a novel family of translationally-invariant su$(m|n)$ spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing the existence of a boson-fermion duality characteristic of this type of systems.
  arXiv  Detail & Related papers  (2024-07-18T18:00:20Z)
• Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
  We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
  arXiv  Detail & Related papers  (2024-06-26T18:27:15Z)
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model [0.0]
  We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$frac12$ XYZ chain. We find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that universally of quantum-chaotic interacting models.
  arXiv  Detail & Related papers  (2023-11-17T19:00:09Z)
• Local Intrinsic Dimensional Entropy [29.519376857728325]
  Most entropy measures depend on the spread of the probability distribution over the sample space $mathcalX|$. In this work, we question the role of cardinality and distribution spread in defining entropy measures for continuous spaces. We find that the average value of the local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust entropy measure for continuous spaces.
  arXiv  Detail & Related papers  (2023-04-05T04:36:07Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems [55.54838930242243]
  Polarizability is a key response property of physical and chemical systems. We show that polarizability follows a universal four-dimensional scaling law. This formula is also applicable to many-particle systems.
  arXiv  Detail & Related papers  (2020-10-22T15:42:36Z)
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions [0.0]
  We show how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. We point out two physically relevant effects that should be easily observed in atomic experiments.
  arXiv  Detail & Related papers  (2020-10-19T19:12:42Z)
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems [0.0]
  We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum.
  arXiv  Detail & Related papers  (2020-08-03T18:00:01Z)
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians [0.0]
  In integrable models, the volume-law coefficient depends on the subsystem fraction. We show that the average entanglement entropy of eigenstates of the power-law random banded matrix model is close but not the same as the result for quadratic models.
  arXiv  Detail & Related papers  (2020-06-19T18:01:15Z)

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.