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Bulletin of the American Physical Society

Thermalization vs. Localization in the Disordered Hubbard Model

William Morong, Wenchao Xu, William McGehee, Brian DeMarco

Published Jun 9, 2015• 0 citations
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Disorder vs. Interaction in the Hubbard Model: Phase Diagram in Infinite Dimensions

V. Janiš, M. Ulmke, D. Vollhardt

The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced

Europhysics Letters (EPL)•Nov 1, 1993•25 citations
Abstract Quantum coherence and phase transitions are studied in a finite one‐dimensional Bose–Hubbard model using exact diagonalization under thermal fluctuations, a Stark potential, and disorder. The condensate fraction, superfluid fraction, visibility, number fluctuations, and the ‐norm of coherence are computed to characterize the Mott insulator–superfluid transition. Although finite‐size effects prevent a sharp transition, ground‐state properties reveal signatures of quantum criticality. Thermal fluctuations can enhance coherence via tunneling, a Stark potential promotes localization, and disorder suppresses global superfluidity while preserving local coherence. These results highlight how disorder, tilt, and temperature reshape coherence and offer insights for quantum simulation and strongly correlated phases. For systems up to six sites with unit filling, a spectral analysis is also performed through the metric mean gap ratio (MGR). However, limited statistics due to the small system size and computational constraints prevent a complete characterization of quantum chaos, yielding only approximate signatures.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced