Area law and universality in the statistics of subsystem energy

Journal Article · Mon Feb 25 00:00:00 EST 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.99.075152· OSTI ID:1612930

Najafi, Khadijeh ^[1]; Rajabpour, M. A. ^[2]

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1. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Georgetown Univ., Washington, DC (United States); DOE/OSTI
2. Univ. Federal Fluminense, Niteroi (Brazil)

We introduce Rényi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all quantum many body systems. In other words, consider a quantum chain in its ground state and then take a subdomain of this system with natural truncated Hamiltonian. Since the total Hamiltonian does not commute with the truncated Hamiltonian, the subsystem can be in one of its eigenenergies with different probabilities. Using the fact that the global energy eigenstates are locally close to diagonal in the local energy eigenbasis, we argue that the Rényi entropy of these probabilities follows an area law for the gapped systems. When the system is at the critical point, the Rényi entropy follows a logarithmic behavior with a universal coefficient. Consequently, our quantity not only detects the phase transition but also determines the universality class of the critical point. Moreover we show that the largest defined probabilities are very close to the biggest Schmidt coefficients. We quantify this by defining a truncated Shannon entropy which its value is almost indistinguishable from the truncated von Neumann entanglement entropy. Compared to the entanglement entropy, our quantity has the advantage of being associated to a natural observable (subsystem Hamiltonian) that can be defined (and probably measured) easily for all the short-range interacting systems. Furthermore, we support our arguments by detailed numerical calculations performed on the transverse field XY chain.

• Research Organization: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
• Sponsoring Organization: National Science Foundation; USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0018326
• OSTI ID: 1612930
• Alternate ID(s): OSTI ID: 1496512
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 7 Vol. 99; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Critical phenomena
Entanglement entropy
Entropy
Materials Science
Physics
Quantum entanglement
Quantum phase transitions
Quantum spin chains
Quantum statistical mechanics