We study the T=0 critical properties of the superfluid-insulator transition in 2D hard core Bose systems with disorder. Using quantum Monte Carlo simulations and finite size scaling on 64\ifmmode\times\else\texttimes\fi{}64 lattices we find the dynamical exponent z=0.5\ifmmode\pm\else\textpm\fi{}0.1 and the correlation length exponent \ensuremath{\nu}=2.2\ifmmode\pm\else\textpm\fi{}0.2. At the transition, the system is metallic with a conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(1.2\ifmmode\pm\else\textpm\fi{}0.2)( ${\mathit{e}}^{\mathrm{*}}$ ${)}^{2}$ /h and a nonzero compressibility \ensuremath{\kappa}\ensuremath{\ne}0. These conclusions differ from the existing scaling theory as well as from simulations on simplified models argued to be in the same universality class. Our results are suggestive of new low lying collective excitations (modified from usual phonons) in the disordered system.We study the T=0 critical properties of the superfluid-insulator transition in 2D hard core Bose systems with disorder. Using quantum Monte Carlo simulations and finite size scaling on 64\ifmmode\times\else\texttimes\fi{}64 lattices we find the dynamical exponent z=0.5\ifmmode\pm\else\textpm\fi{}0.1 and the correlation length exponent \ensuremath{\nu}=2.2\ifmmode\pm\else\textpm\fi{}0.2. At the transition, the system is metallic with a conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(1.2\ifmmode\pm\else\textpm\fi{}0.2)(${\mathit{e}}^{\mathrm{*}}$${)}^{2}$/h and a nonzero compressibility \ensuremath{\kappa}\ensuremath{\ne}0. These conclusions differ from the existing scaling theory as well as from simulations on simplified models argued to be in the same universality class. Our results are suggestive of new low lying collective excitations (modified from usual phonons) in the disordered system.

Physical Review LettersOct 4, 199394 citations

Ergodicity breaking and restoring in disordered quantum systems

Giacomo Bracci-Testasecca

Understanding the effects of disorder in quantum many-body systems is one of the central challenges of contemporary statistical physics. Its interplay with interactions and quantum fluctuations profoundly modifies the nature of quantum states and their dynamics, giving rise to phenomena such as localization, ergodicity breaking, and the emergence of complex collective behavior. This thesis presents new results on two classes of disordered quantum systems. The first part is devoted to the study of the many-body localization transition, a paradigmatic example of disorder-induced ergodicity breaking. The critical properties of the transition are investigated using a numerical renormalization-group approach, establishing a connection between its scaling behavior and that of the Anderson localization transition on tree-like graphs. The second part focuses on the zero-temperature quantum spin-glass phase of the two-dimensional bond-disordered Heisenberg model. Combining large-scale numerical simulations with a semiclassical expansion, evidence is provided for the existence of the spin-glass phase. The effective model governing the semiclassical fluctuations is further analyzed to characterize the low-energy excitation spectrum and its localization properties. Finally, the weak-disorder regime is investigated and its implications for the ferromagnetic phase are discussed. Overall, the results presented in this thesis contribute to the understanding of the effects of disorder in interacting quantum many-body systems, encompassing both localization phenomena and the collective behavior of disordered quantum magnets.Understanding the effects of disorder in quantum many-body systems is one of the central challenges of contemporary statistical physics. Its interplay with interactions and quantum fluctuations profoundly modifies the nature of quantum states and their dynamics, giving rise to phenomena such as localization, ergodicity breaking, and the emergence of complex collective behavior. This thesis presents new results on two classes of disordered quantum systems. The first part is devoted to the study of the many-body localization transition, a paradigmatic example of disorder-induced ergodicity breaking. The critical properties of the transition are investigated using a numerical renormalization-group approach, establishing a connection between its scaling behavior and that of the Anderson localization transition on tree-like graphs. The second part focuses on the zero-temperature quantum spin-glass phase of the two-dimensional bond-disordered Heisenberg model. Combining large-scale numerical simulations with a semiclassical expansion, evidence is provided for the existence of the spin-glass phase. The effective model governing the semiclassical fluctuations is further analyzed to characterize the low-energy excitation spectrum and its localization properties. Finally, the weak-disorder regime is investigated and its implications for the ferromagnetic phase are discussed. Overall, the results presented in this thesis contribute to the understanding of the effects of disorder in interacting quantum many-body systems, encompassing both localization phenomena and the collective behavior of disordered quantum magnets.

Sep 21, 20260 citations

Ground state and excitations of disordered boson systems

Michael Ma, Pornthep Nisamaneephong, Lizeng Zhang

arXiv:cond-mat/9311007Journal of Low Temperature PhysicsDec 1, 199311 citations

a Study of the Disordered Boson Systems

Lizeng Zhang

Jan 1, 19900 citations

Bosonic excitations in random media

Victor Gurarie, J. T. Chalker

We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.

arXiv:cond-mat/0305445Physical review. B, Condensed matterOct 15, 2003144 citations

{\mathit{e}}^{\mathrm{*}}

{)}^{2}

/h and a nonzero compressibility \ensuremath{\kappa}\ensuremath{\ne}0. These conclusions differ from the existing scaling theory as well as from simulations on simplified models argued to be in the same universality class. Our results are suggestive of new low lying collective excitations (modified from usual phonons) in the disordered system.

{d}_{c},

which in different circumstances takes the values

{d}_{c}=2

and

{d}_{c}=0.

For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.