期刊
PHYSICAL REVIEW B
卷 93, 期 12, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.93.125128
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资金
- NSF PIF
- AFOSR
- ARO
- ARL
- NSF PFC at the JQI
- AFOSR MURI
- NRC
- Division Of Physics
- Direct For Mathematical & Physical Scien [1430094, 1415616] Funding Source: National Science Foundation
Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model with long-range interactions, and a fermionic model with long-range hopping and pairing terms, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of the long-range couplings, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent.
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