Zero Curvature Condition for Quantum Criticality
- URL: http://arxiv.org/abs/2303.09591v1
- Date: Thu, 16 Mar 2023 18:35:19 GMT
- Title: Zero Curvature Condition for Quantum Criticality
- Authors: Chaoming Song
- Abstract summary: We present a new paradigm of quantum criticality based on a novel geometric approach.
We demonstrate that the quantum phase transition occurs precisely at the zero-curvature point on this boundary.
- Score: 1.261852738790008
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum criticality typically lies outside the bounds of the conventional
Landau paradigm. Despite its significance, there is currently no generic
paradigm to replace the Landau theory for quantum phase transition, partly due
to the rich variety of quantum orders. In this paper, we present a new paradigm
of quantum criticality based on a novel geometric approach. Instead of focusing
on microscopic orderings, our approach centers on the competition of commuting
operators, which can be best investigated through the boundary geometry of
their expectation values. We demonstrate that the quantum phase transition
occurs precisely at the zero-curvature point on this boundary, which implies
the competing operators are maximally commuting at the critical point.
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