Measuring Topological Field Theories: Lattice Models and Field-Theoretic Description

• URL: http://arxiv.org/abs/2310.17740v1
• Date: Thu, 26 Oct 2023 19:26:04 GMT
• Title: Measuring Topological Field Theories: Lattice Models and Field-Theoretic Description
• Authors: Yabo Li, Mikhail Litvinov, Tzu-Chieh Wei
• Abstract summary: Recent years have witnessed a surge of interest in performing measurements within topological phases of matter. We present a field-theoretic framework for describing measurements within topological field theories.
• Score: 2.541410020898643
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent years have witnessed a surge of interest in performing measurements within topological phases of matter, e.g., symmetry-protected topological (SPT) phases and topological orders. Notably, measurements of certain SPT states have been known to be related to Kramers-Wannier duality and Jordan-Wigner transformations, giving rise to long-range entangled states and invertible phases, such as the Kitaev chain. Moreover, measurements of topologically ordered states correspond to charge condensations. In this work, we present a field-theoretic framework for describing measurements within topological field theories. We employ various lattice models as examples to illustrate the outcomes of measuring local symmetry operators within topological phases, demonstrating their agreement with the predictions from field-theoretic descriptions. We demonstrate that these measurements can lead to SPT, spontaneous symmetry-breaking, and topologically ordered phases. Specifically, when there is emergent symmetry after measurement, the remaining symmetry and emergent symmetry will have a mixed anomaly, which leads to long-ranged entanglement.

Related papers

• Long-range entanglement from spontaneous non-onsite symmetry breaking [3.3754780158324564]
  We show a frustration-free lattice model exhibiting SSB of a non-onsite symmetry. We analytically prove the two-fold ground-state degeneracy and the existence of a finite energy gap. Our work reveals the exotic features of SSB of non-onsite symmetries, which may lie beyond the framework of topological holography.
  arXiv  Detail & Related papers  (2024-11-07T18:59:51Z)
• Gauge theory and mixed state criticality [0.0]
  In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. We present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models.
  arXiv  Detail & Related papers  (2024-11-07T01:40:56Z)
• Cahier de l'Institut Pascal: Noisy Quantum Dynamics and Measurement-Induced Phase Transitions [44.99833362998488]
  We provide an analysis of recent results in the context of measurement-induced phase transitions in quantum systems. Recent results show how varying the rate of projective measurements can induce phase transitions. We present results on the non-local effects of local measurements by examining the field theory of critical ground states in Tomonaga-Luttinger liquids.
  arXiv  Detail & Related papers  (2024-09-10T08:10:25Z)
• Multipole and fracton topological order via gauging foliated SPT phases [0.0]
  In accordance with the progress of multipole symmetries, there have been proposed topological phases with such symmetries. These topological phases are unconventional as excitations are subject to mobility constraints corresponding to the multipole symmetries. We demonstrate a way to construct such phases by preparing layers of symmetry protected topological phases and implementing gauging a global symmetry.
  arXiv  Detail & Related papers  (2024-01-19T13:19:40Z)
• Action formalism for geometric phases from self-closing quantum trajectories [55.2480439325792]
  We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
  arXiv  Detail & Related papers  (2023-12-22T15:20:02Z)
• Exploring critical systems under measurements and decoherence via Keldysh field theory [0.0]
  We employ an $n$-replica Keldysh field theory to investigate the effects of measurements and decoherence on long distance behaviors of quantum critical states. Low energy effective theories for various scenarios are then derived using the symmetry and fundamental consistency conditions of the Keldysh formalism. Our results demonstrate that the Keldysh formalism is a useful tool for systematically studying the effects of measurements and decoherence on long-wavelength physics.
  arXiv  Detail & Related papers  (2023-04-17T13:48:09Z)
• Topological transitions of the generalized Pancharatnam-Berry phase [55.41644538483948]
  We show that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. We demonstrate and study this transition experimentally employing an optical platform. Our protocol can be interpreted in terms of environment-induced geometric phases.
  arXiv  Detail & Related papers  (2022-11-15T21:31:29Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• 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)
• Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases [55.41644538483948]
  Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. Our results open new horizons for measurement-enabled quantum control of many-body topological states.
  arXiv  Detail & Related papers  (2021-02-10T19:00:00Z)
• Weak-measurement-induced phases and dephasing: broken symmetry of the geometric phase [1.4174475093445233]
  Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. Superseding common wisdom, we show that the symmetric and the antisymmetric components do not correspond to the dynamical and geometrical parts respectively. We find transitions between different topologically distinct sectors, defined by integer-valued winding numbers, and show that the transitions are accompanied by diverging dephasing.
  arXiv  Detail & Related papers  (2020-06-25T18:03:55Z)

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.