Time development of quantum lattice systems

Mario Pulvirenti, Brunello Tirozzi

Shohei Kashiwamura

Statistical dynamical feature of time development of one-dimensional harmonic lattice containing a few impurities is investigated. The fundamental solutions of equations of motion are obtained for a system of a finite number of particles as well as that of an infinite number of particles. The difference between those solutions is not appreciable at least within a range of time. Next, such an initial ensemble is introduced that a part of the lattice is canonically distributed with temperature T0 and the remaining part remains quite at rest. It is shown that the ensemble approaches a stationary state in a small sub-system for a more limited range of time. In the stationary state the mean energy of each particle is expressed as a function of characteristic parameters of the impurity particles.

Yu. G. Kondrat’ev

Chris Culver, David Schaich

Quantum computing promises the possibility of studying the real-time dynamics of non-perturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices are severely limited by noise, making investigations of simple low-dimensional lattice systems ideal testbeds for algorithm development. Considering simple supersymmetric systems, such as supersymmetric quantum mechanics with different superpotentials, allows for the analysis of phenomena like dynamical supersymmetry breaking. We present ongoing work applying quantum computing techniques to study such theories, targeting real-time dynamics and supersymmetry breaking effects.

Rui Xie, Clemens Gneiting, Zheng-Yang Zhou +1 more

The topological properties of open quantum lattice systems have attracted much attention, due to their fundamental significance and potential applications. However, experimental demonstrations with large-scale lattice models remain challenging. On top of that, formulations of topology in terms of quantum trajectories require monitoring along with the detection of quantum jumps. This is particularly the case for the dark state-induced topology that relies on averaging quantum trajectories at their jump times. Here, we propose two significant simplifications to ease the experimental burden to demonstrate dark-state induced topological phase transitions: First, we emulate the topology in the phase space of small systems, where the effective size of the system is reflected by the accessible parameter range. Second, we develop a method how to, by augmenting the system with an auxiliary system, access the jump-time averaged state through standard wall-time averaging, which effectively substitutes the monitoring along with the counting of quantum jumps. While these simplifications are applicable to general lattice systems, we demonstrate them with a one-dimensional Su-Schrieeffer-Heeger model. In this case, the lattice system is emulated by a four-level system, while the jump-time averaged state up to the second jump is accessed through a three-level auxiliary system.

Mitchel Weissbluth