A survey of quantum hardware platforms and methods for simulating condensed matter physics, covering ground states, topology, non-equilibrium dynamics, and the role of noisy devices as prototypes for fault-tolerant simulation.
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
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abstract
We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.
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Simulating Condensed Matter Physics on Quantum Hardware
A survey of quantum hardware platforms and methods for simulating condensed matter physics, covering ground states, topology, non-equilibrium dynamics, and the role of noisy devices as prototypes for fault-tolerant simulation.