TY - JOUR

T1 - Quantized gravitational responses, the sign problem, and quantum complexity

AU - Ringel, Zohar

AU - Kovrizhin, Dmitry L.

N1 - Publisher Copyright:
Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.

PY - 2017

Y1 - 2017

N2 - It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question—whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems—remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved.

AB - It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question—whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems—remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved.

UR - http://www.scopus.com/inward/record.url?scp=85041839303&partnerID=8YFLogxK

U2 - 10.1126/sciadv.1701758

DO - 10.1126/sciadv.1701758

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C2 - 28959729

AN - SCOPUS:85041839303

SN - 2375-2548

VL - 3

JO - Science advances

JF - Science advances

IS - 9

M1 - 1701758

ER -