Adiabatic landscape and optimal paths in ergodic systems
- URL: http://arxiv.org/abs/2004.13735v1
- Date: Tue, 28 Apr 2020 18:00:04 GMT
- Title: Adiabatic landscape and optimal paths in ergodic systems
- Authors: Sho Sugiura, Pieter W. Claeys, Anatoly Dymarsky, Anatoli Polkovnikov
- Abstract summary: We find optimal paths in the space of couplings controlling the system's Hamiltonian.
We identify robust weakly-thermalizing and non-absorbing many-body "dark" states which are annihilated by the singular part of the AGP.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Whether one is interested in quantum state preparation or in the design of
efficient heat engines, adiabatic (reversible) transformations play a pivotal
role in minimizing computational complexity and energy losses. Understanding
the structure of these transformations and identifying the systems for which
such transformations can be performed efficiently and quickly is therefore of
primary importance. In this paper we focus on finding optimal paths in the
space of couplings controlling the system's Hamiltonian. More specifically,
starting from a local Hamiltonian we analyze directions in the space of
couplings along which adiabatic transformations can be accurately generated by
local operators, which are both realizable in experiments and easy to simulate
numerically. We consider a non-integrable 1D Ising model parametrized by two
independent couplings, corresponding to longitudinal and transverse magnetic
fields. We find regions in the space of couplings characterized by a very
strong anisotropy of the variational adiabatic gauge potential (AGP),
generating the adiabatic transformations, which allows us to define optimal
adiabatic paths. We find that these paths generally terminate at singular
points characterized by extensive degeneracies in the energy spectrum,
splitting the parameter space into adiabatically disconnected regions. The
anisotropy follows from singularities in the AGP, and we identify special
robust weakly-thermalizing and non-absorbing many-body "dark" states which are
annihilated by the singular part of the AGP and show that their existence
extends deep into the ergodic regime.
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