Journal
PHYSICAL REVIEW X
Volume 4, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.4.011052
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Funding
- National Science Foundation [NSF PHY11-25915]
- NSF [1066293]
- FAS Science Division Research Computing Group at Harvard University
- Lee A. DuBridge prize postdoctoral fellowship
- IQIM
- Moore Foundation [DMR-0955714]
- Packard Foundation
- BSF
- ISF
- Miller Institute for Basic Science
- Harvard-MIT CUA
- DARPA OLE program
- AFOSR MURI on Ultracold Molecules
- ARO-MURI on Atomtronics
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [0955714] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Physics [1125846] Funding Source: National Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1125565] Funding Source: National Science Foundation
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We study a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. One example of such a transition is the recently proposed many-body localization-delocalization transition, in which transport coefficients vanish at a critical temperature with no singularities in thermodynamic observables. Describing this purely dynamical quantum criticality is technically challenging as understanding the finite-temperature dynamics necessarily requires averaging over a large number of matrix elements between many-body eigenstates. Here, we develop a real-space renormalization group method for excited states that allows us to overcome this challenge in a large class of models. We characterize a specific example: the 1 D disordered transverse-field Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the real-space renormalization group method for excited states we find a finite-temperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the low-frequency heat conductivity and in the long-time (dynamic) spin correlation function. The latter is a consequence of an up-down spin symmetry that results in the appearance of an Edwards-Anderson-like order parameter in one of the localized phases.
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