Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives

• URL: http://arxiv.org/abs/2009.05064v1
• Date: Thu, 10 Sep 2020 18:01:19 GMT
• Title: Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives
• Authors: C. L. Baldwin, S. Shivam, S. L. Sondhi, M. Kardar
• Abstract summary: We show that phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

Related papers

• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• 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)
• Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models [0.0]
  Non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians. We show that the dynamics of the OAT model can be closely reproduced by systems with power-lawdecaying interactions.
  arXiv  Detail & Related papers  (2023-02-18T09:37:45Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
  We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
  arXiv  Detail & Related papers  (2022-07-14T10:05:20Z)
• Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
  We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model. The two-mode Dicke model exhibits normal to superradiant quantum phase transition. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
  arXiv  Detail & Related papers  (2022-07-08T11:16:29Z)
• Emergent tracer dynamics in constrained quantum systems [0.0]
  We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions.
  arXiv  Detail & Related papers  (2022-05-16T18:00:02Z)
• Multipartite correlations in quantum collision models [0.0]
  A challenge in the standard collision model is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Here we develop a tensor network formalism to address both challenges. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory- kernel master equation.
  arXiv  Detail & Related papers  (2022-04-05T17:06:27Z)
• Distinct universality classes of diffusive transport from full counting statistics [0.4014524824655105]
  We study the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian universality class. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.
  arXiv  Detail & Related papers  (2022-03-17T18:00:01Z)
• Subdiffusion via Disordered Quantum Walks [52.77024349608834]
  We experimentally prove the feasibility of disordered quantum walks to realize a quantum simulator that is able to model general subdiffusive phenomena. Our experiment simulates such phenomena by means of a finely controlled insertion of various levels of disorder during the evolution of the walker. This allows us to explore the full range of subdiffusive behaviors, ranging from anomalous Anderson localization to normal diffusion.
  arXiv  Detail & Related papers  (2020-07-24T13:56:09Z)

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.