Long Range Dynamics and Spontaneous Symmetry Breaking in Many-Body Systems

G. Morchio, Franco Strocchi

The algebraic dynamics of systems with long-range (instantaneous) interactions requires an enlargement of the (quasi) local algebra which, in most relevant cases, includes variables at infinity that enter in an essential way in the time evolution of local variables. The mathematical structures emerging for the treatment of long-range dynamics are investigated also in connection with spontaneous symmetry breaking.

Spartak T. Belyaev

Filippo Caleca, Saverio Bocini, Fabio Mezzacapo +1 more

Spontaneous symmetry breaking (SSB) occurs when a many-body system governed by a symmetric Hamiltonian, and prepared in a symmetry-broken state by the application of a field coupling to its order parameter O, retains a finite O value even after the field is switched off. SSB is generally thought to occur only in the thermodynamic limit N→∞ (for N degrees of freedom). In this limit, the time to restore the symmetry once the field is turned off, either via thermal or quantum fluctuations, is expected to diverge. Here, we show that SSB can also be observed in finite-size quantum spin systems, provided that the spin is half-integer and three conditions are met: (1) the ground state of the system has long-range correlations, (2) the Hamiltonian conserves the (spin) parity of the order parameter, and (3) N is odd. Using a combination of analytical arguments and numerical results (based on time-dependent variational Monte Carlo and rotor + spin-wave theory), we show that SSB on finite-size systems can be achieved via a quasiadiabatic preparation of the ground state-which, in U(1)-symmetric systems, is shown to require a symmetry-breaking field vanishing over timescales τ∼O(N). In these systems, the symmetry-broken state exhibits spin squeezing with Heisenberg scaling.

Anton S. Buyskikh

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

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.

董国慧, 房一楠, 孙昌璞