Entanglement entropy of theQ<mml:mspace width="0.16em"/>≥<mml:mspace width="0.16em"/>4quantum Potts chain

2016/08/17 by Péter Lajkó, Ferenc Iglói
Computer Science · Physics and Astronomy · #Algorithm #Computer science #Entropy (arrow of time) #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.95.012105

published as Phys. Rev. E 95, 012105 (2017)

arxiv created 2016/08/17 · openalex created_date 2016/09/16 · openalex publication_date 2017/01/04 · arxiv updated 2017/01/11 · openalex updated_date 2026/08/05

Abstract

The entanglement entropy S is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension S generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the Q-state quantum Potts chain for Q&gt;4 and calculate S across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point S shows a jump, which is expected to vanish for Q\ensuremath→4⁺. This jump is calculated in leading order as \mathrm\ensuremathΔS=lnQ[1\ensuremath-4/Q\ensuremath-2/(QlnQ)+O(1/Q²)].

Citations

• Colloquium: Area laws for the entanglement entropy
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Entanglement Negativity in Quantum Field Theory
• Dynamics of a quantum phase transition and relaxation to a steady state
• Disorder Induced Cross-Over Effects at Quantum Critical Points
• On single-copy entanglement
• Density-matrix algorithms for quantum renormalization groups
• Entanglement in theXYspin chain
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Separability Criterion for Density Matrices
• Entanglement entropy of quantum wire junctions
• Density profiles, Casimir amplitudes, and critical exponents in the two-dimensional Potts model: A density-matrix renormalization study
• Calculation of reduced density matrices from correlation functions
• Entanglement spectrum of a topological phase in one dimension
• Entanglement entropy of the randoms=1Heisenberg chain
• Evolution of entanglement after a local quench
• Entanglement entropy of aperiodic quantum spin chains
• Entanglement in many-body systems