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arXiv:2012.07243 · PRX Quantum

Collisions of False-Vacuum Bubble Walls in a Quantum Spin Chain

Ashley Milsted, Junyu Liu, John Preskill, Guifré Vidal

Published Apr 22, 2022• 78 citations
arXivHTMLPDF

Abstract

We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about 1000 spins embedded in an infinite chain at energies of up to about 5 times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.

DOI
10.1103/prxquantum.3.020316

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We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about 1000 spins embedded in an infinite chain at energies of up to about 5 times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.
The false vacuum decay has been a central theme in physics for half a century with applications to cosmology and to the theory of fundamental interactions. This fascinating phenomenon is even more intriguing when combined with the confinement of elementary particles. Due to the astronomical timescales involved, the research has so far focused on theoretical aspects of this decay. The purpose of this Letter is to show that the false vacuum decay is accessible to current optical experiments as quantum analog simulators of spin chains with confinement of the elementary excitations, which mimic the high energy phenomenology but in one spatial dimension. We study the nonequilibrium dynamics of the false vacuum in a quantum Ising chain and in an XXZ ladder. The false vacuum is the metastable state that arises in the ferromagnetic phase of the model when the symmetry is explicitly broken by a longitudinal field. This state decays through the formation of ``bubbles'' of true vacuum. Using infinite volume time evolving block decimation (iTEBD) simulations, we are able to study the real-time evolution in the thermodynamic limit and measure the decay rate of local observables. We find that the numerical results agree with the theoretical prediction that the decay rate is exponentially small in the inverse of the longitudinal field.
Recent real-time simulations of false-vacuum decay in the quantum Ising chain report decay-rate prefactors that disagree with each other and with field theory by factors up to three. We prepare the metastable state by a real-time ramp of the longitudinal field, measure the survival rate per site of an infinite matrix-product state, and compare it with the decay rate that Fonseca and Zamolodchikov obtained from the free energy of the Ising field theory continued to negative field. At two lattice spacings and scaling variables y = 2.2–2.8 the ratio is 1.008 with a standard deviation of 0.015 over 6 runs, with no adjustable parameter, once the first correction to the thin-wall formula is kept. The two-kink coefficient π∆E/18 used in recent comparisons is too large by π2/9, as anticipated by Fonseca and Zamolodchikov, and exponential fits to the order parameter return rates 147–390 times larger than the nucleation rate. The survival rate, or equivalently the growth rate of the bubble density, is the observable that quantum simulators should compare with theory.
We study scattering in the quantum Ising model in two dimensions. In the ordered phase, the spectrum contains a ladder of bound states and intertwined scattering resonances, which enable various scattering channels. By preparing wave packets on a 24 × 24 lattice and evolving the state with tensor networks, we explore and characterize these regimes, ranging from elastic scattering in the perturbative regime, to non-perturbative processes closer to the critical point. Then, we break the spin inversion symmetry and study the stability of the metastable false vacuum state on the collision of its excitations. We find that a highly-energetic scattering process can induce a violent decay of the false vacuum, and investigate the spread of the resulting true vacuum bubble. Spin chains enable quantum simulation of scattering-related phenomena of interest for highenergy- and condensed-matter-physics, yet current approaches are limited to low dimensional cases. Here, the authors address this gap by studying magnon scattering in 2D quantum Ising models via tree tensor networks. This unveils new resonances and induced false vacuum decay dynamics.
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Extracting a thermodynamic nucleation rate from finite-time quantum dynamics requires separating observable decay from estimator and finite-size validity. We develop a multilevel identification framework for real-time tensor-network simulations of false-vacuum decay in the one-dimensional quantum Ising chain. Across twelve parameter points, the same coherent two-kink amplitudes semi-quantitatively predict both infinite-chain survival and magnetization dynamics: the survival coefficient has a median lattice-to-theory ratio of 0.896, while the magnetization-area slope ratios span 0.767--0.931. By contrast, the microscopic nearest-neighbour bond response is coherence dominated: vacuum--pair coherence contributes 60.0--81.5% across seven points with matched bond-dimension control, while substantial late-window slope discrepancies remain that cannot be removed by a scalar normalization. The analysis establishes finite-time survival and magnetization benchmarks and identifies the additional finite-size and branch-validation requirements for a bulk thermodynamic rate interpretation. Within the two-kink model and under the adopted common normalization, the lattice-resolved WKB action gives a median fixed-prefactor rate discrepancy of 4.13% from the coherent-bubble spectral calculation. These results distinguish finite-time lattice--theory consistency from the additional observable and finite-size evidence required to identify a thermodynamic nucleation rate.
In this work we characterize the false vacuum decay in the ferromagnetic quantum Ising chain with a weak longitudinal field subject to continuous monitoring of the local magnetization. Initializing the system in a metastable state, the false vacuum, we study the competition between coherent dynamics, which tends to create resonant bubbles of the true vacuum, and measurements which induce heating and reduce the amount of quantum correlations. To this end we exploit a numerical approach based on the combination of matrix product states with stochastic quantum trajectories which allows for the simulation of the trajectory-resolved non-equilibrium dynamics of interacting many-body systems in the presence of continuous measurements. We show how the presence of measurements affects the false vacuum decay: At short times the departure from the local minimum is accelerated while at long times the system thermalizes to an infinite-temperature incoherent mixture. For large measurement rates the system enters a quantum Zeno regime. The false vacuum decay and the thermalization physics are characterized in terms of the magnetization, connected correlation function, and the trajectory-resolved entanglement entropy.