2020/01/28 by Abhisek Samanta, Kedar Damle, Rajdeep Sensarma
Mathematics · Physics and Astronomy · #Degrees of freedom (physics and chemistry) #Eigenvalues and eigenvectors #Ergodic theory #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Phase (matter) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Qubit #Spectrum (functional analysis) #Thermalisation #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.104201
published as Phys. Rev. B 102, 104201 (2020)
arxiv created 2020/01/28 · openalex created_date 2020/02/07 · openalex publication_date 2020/09/02 · arxiv updated 2020/09/09 · openalex updated_date 2026/08/05
Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body spectrum) exhibit a qualitative change across this many-body localization (MBL) transition, many of the commonly used diagnostics only do so over a broad transition regime. Here we provide evidence that the transition can be located precisely even at modest system sizes by sharply defined changes in the distribution of extremal eigenvalues of the reduced density matrix of subsystems. In particular, our results suggest that p*=lim_\ensuremathλ2\ensuremath→ln(2)+P2(\ensuremathλ2), where P2(\ensuremathλ2) is the probability distribution of the second lowest entanglement eigenvalue \ensuremathλ2, behaves as an ``order parameter'' for the MBL phase: p*>0 in the MBL phase, while p*=0 in the ergodic phase with thermalization. Thus, in the MBL phase, there is a nonzero probability that a subsystem is entangled with the rest of the system only via the entanglement of one subsystem qubit with degrees of freedom outside the region. In contrast, this probability vanishes in the thermal phase.