Interacting spins in a cavity: finite size effects and symmetry-breaking dynamics

Abstract

We calculate the ground state and simulate the dynamics of a finite chain of spins with Ising nearest-neighbor interactions and a Dicke collective spin interaction with a single mode cavity field. We recover the signatures of first and second order phase transitions predicted by mean field theory, while for small chains, we find significant and non-trivial finite size effects. Below the first order phase transition, even quite large spin chains of 30-40 spins give rise to a mean photon number and number fluctuations significantly above the mean field vacuum result. Near the second order phase critical point, our calculations reveal photon number fluctuations that grow beyond Poisson statistics with the size of the spin chain. We simulate the stochastic evolution of the system when the cavity output field is subject to homodyne detection. For an initial state close to the first order phase-transition the random character of the measurement process causes a measurement-induced symmetry-breaking in the system. This symmetry-breaking occurs on the time-scale needed for an observer to gather sufficient information to distinguish between the two possible (mean-field) symmetry-broken states.

arXiv comment7 pages, 4 figures

References in corpus (19)

• The density-matrix renormalization group
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• A class of quantum many-body states that can be efficiently simulated
• Criticality, the area law, and the computational power of PEPS
• A Straightforward Introduction to Continuous Quantum Measurement
• Matrix product operator representations
• PEPS as ground states: degeneracy and topology
• Quantum Trajectories and Quantum Measurement Theory
• Renormalization group transformations on quantum states
• Time evolution algorithms for Matrix Product States and DMRG
• Exact dynamics in the inhomogeneous central-spin model
• Linear stochastic wave-equations for continuously measured quantum systems
• Phase transitions in an Ising chain interacting with a single mode cavity field
• Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation
• First-order super-radiant phase transitions in a multi-qubit--cavity system
• Dynamics and decoherence in the central spin model using exact methods
• Circuit QED and sudden phase switching in a superconducting qubit array
• Simulating local measurements on a quantum many body system with stochastic matrix product states

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• Theoretical methods to treat a single dissipative bosonic mode coupled globally to an interacting many body system
• Polariton spectrum of the Dicke-Ising model
• The effect of atomic collisions on the quantum phase transition of a Bose-Einstein condensate inside an optical cavity
• Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation