Spontaneous Symmetry Breaking Induced by Quantum Monitoring

Luis Pedro García-Pintos, Diego Tielas, and Adolfo del Campo

Phys. Rev. Lett. 123, 090403 – Published 29 August 2019

Abstract

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements. The acquisition of information during the measurement process induces a measurement backaction that seeds SSB. In this setting, by monitoring different observables, an observer can tailor the topology of the vacuum manifold, the pattern of symmetry breaking, and the nature of the resulting domains and topological defects.

Received 24 November 2018
Revised 20 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.090403

Physics Subject Headings (PhySH)

Phase transitions Quantum measurements Spontaneous symmetry breaking

Quantum spin models

Quantum Information, Science & Technology

Authors & Affiliations

Luis Pedro García-Pintos^1,*, Diego Tielas^1,2,3,†, and Adolfo del Campo^4,5,1,6,‡

¹Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
²IFLP, CONICET-Department of Physics, University of La Plata, C.C. 67 (1900), La Plata, Argentina
³Faculty of Engineering, University of La Plata, B1900 La Plata, Argentina
⁴Donostia International Physics Center, E-20018 San Sebastián, Spain
⁵IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
⁶Theoretical Division, Los Alamos National Laboratory, MS-B213, Los Alamos, New Mexico 87545, USA

^*Corresponding author. luis.garciapintos@umb.edu
^†tielas@fisica.unlp.edu.ar
^‡adolfo.delcampo@umb.edu

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Issue

Vol. 123, Iss. 9 — 30 August 2019

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Images

Figure 1
From single spin to coarse-grained monitoring. The nature of the monitoring process determines the pattern of measurement-induced symmetry breaking, deciding the size of the domains, the distribution of the local magnetization, and the type of topological defects formed in the system. (a) Independent observers measuring each single spin induce random, independent measurement outcomes for each spin, which end up either “up” or “down.” (b) Independent observers measuring the magnetization of clusters of spins provoke the formation of local and independent domains, which can take different values of the magnetization. (c) In the limiting case of one single observer measuring the whole spin chain, the induced global magnetization due to quantum monitoring is homogeneous.
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Figure 2
Dynamics of symmetry breaking induced by monitoring of each spin for different measurement strengths. (a) A weak monitoring of the individual spins slightly affects their spin components, barely perturbing the otherwise symmetric evolution. (b) As the measurement strength is increased symmetry is broken by the measurement process, leading to spins collapsing to the stable up or down configurations. (c) A strong monitoring process rapidly leads to the formation of localized topological defects in individual realizations of the stochastic evolution.
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Figure 3
Monitoring-induced symmetry breaking for a slow quench. A system undergoing a slow quench ( $1 / τ_{Q} ≪ Λ$ ) tends to remain close to the ground state, but in the absence of monitoring and other sources of symmetry breaking the system cannot select between degenerate ferromagnetic ground states $| ↑ ↑ \dots ↑ ↑ ⟩$ and $| ↓ ↓ \dots ↓ ↓ ⟩$ . (a) A strong monitoring of the individual spins ( $1 / τ_{m} \sim 1 / τ_{Q} ≪ Λ$ ) generates a symmetry broken state where spins are uncorrelated. (b) A weak monitoring ( $1 / τ_{m} ≪ {Λ, 1 / τ_{Q}}$ ) leads to an almost uniform domain, and a final state that is close to one of the possible symmetry-broken ground states of the ferromagnetic Hamiltonian.
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Figure 4
Evolution of $⟨ σ_{j}^{z} ⟩$ for coarse-grained measurements. (a) The continuous monitoring of the coarse-grained local magnetization breaks the symmetry, resulting in the formation of independent domains. For independent observers monitoring the local magnetization over the spin chain, the typical size of the domains is determined by the number of spins $K$ over which the independent measurement operators $m_{α}$ act on. Moreover, the stable final states within each domain need not correspond to all spins pointing up or down, as $m_{α}$ can take ( $K + 1$ ) different values. (b) In the extremal case of one observer monitoring the global magnetization, a single domain is formed. The nature of the monitoring process thus governs structure formation in the final state.
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