In this thesis, we consider two different topics: the probes of out-of-equilibrium topological matter and many-body-localization (MBL) in higher dimensions. The first part focuses on the two-dimensional (2D) topological Floquet p+ip superfluid induced by an instantaneous quench of the interaction strength. We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of this out-of-equilibrium quantum system in both the cold-atomic and solid-state realizations. We notice a single avoided crossing in the Floquet band structure and a population inversion in the occupation of these bands. In addition, the rf spectrum is well captured by a quasiequilibrium approximation and shows a robust gap. We also compute the rf signal when only the lower Floquet band is occupied as well as the tunneling signal. In both cases, the spectra show wildly different behaviors compared with the rf signal from the post-quench state, and the gap disappears for strong quenches. We attribute this to the fact that the distribution function influences the rf but not the tunneling signal. Finally, we look into the ARPES spectrum which exhibits a clear series of Floquet copies. The second part is devoted to interacting fermions in the presence of quenched disorder. We derive a finite-temperature Keldysh response theory for such a system in the delocalized phase, in the form of the Finkel'stein nonlinear sigma model (FNLσM). Applicable to any symmetry class with at least a U(1) symmetry, our formulation automatically incorporates the correct infrared cutoffs for quantum corrections to transport, and provides a framework to study the real and virtual scattering processes. In particular, we are able to rederive from the FNLσM the Altshuler-Aronov-Khmelnitsky equations for dephasing. We then propose a strategy to approach the 2D ergodic-to-MBL transition from the ergodic side. Such a transition is explored as a dephasing catastrophe in an isolated system with short-range interactions. In this case, the self-generated heat bath responsible for dephasing exhibits diffusive (non-Markovian) density fluctuations. We recast the dephasing of quantum interference corrections as a self-interacting polymer loop, and study its critical behavior using renormalization group approach. In dimensions d=4-ε, we identify a nontrivial fixed point corresponding to a finite temperature where the dephasing time diverges. This fixed point can be associated with a toy version of 2D ergodic-to-MBL transition, provided that it survives to ε=2.In this thesis, we consider two different topics: the probes of out-of-equilibrium topological matter and many-body-localization (MBL) in higher dimensions. The first part focuses on the two-dimensional (2D) topological Floquet p+ip superfluid induced by an instantaneous quench of the interaction strength. We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of this out-of-equilibrium quantum system in both the cold-atomic and solid-state realizations. We notice a single avoided crossing in the Floquet band structure and a population inversion in the occupation of these bands. In addition, the rf spectrum is well captured by a quasiequilibrium approximation and shows a robust gap. We also compute the rf signal when only the lower Floquet band is occupied as well as the tunneling signal. In both cases, the spectra show wildly different behaviors compared with the rf signal from the post-quench state, and the gap disappears for strong quenches. We attribute this to the fact that the distribution function influences the rf but not the tunneling signal. Finally, we look into the ARPES spectrum which exhibits a clear series of Floquet copies. The second part is devoted to interacting fermions in the presence of quenched disorder. We derive a finite-temperature Keldysh response theory for such a system in the delocalized phase, in the form of the Finkel'stein nonlinear sigma model (FNLσM). Applicable to any symmetry class with at least a U(1) symmetry, our formulation automatically incorporates the correct infrared cutoffs for quantum corrections to transport, and provides a framework to study the real and virtual scattering processes. In particular, we are able to rederive from the FNLσM the Altshuler-Aronov-Khmelnitsky equations for dephasing. We then propose a strategy to approach the 2D ergodic-to-MBL transition from the ergodic side. Such a transition is explored as a dephasing catastrophe in an isolated system with short-range interactions. In this case, the self-generated heat bath responsible for dephasing exhibits diffusive (non-Markovian) density fluctuations. We recast the dephasing of quantum interference corrections as a self-interacting polymer loop, and study its critical behavior using renormalization group approach. In dimensions d=4-ε, we identify a nontrivial fixed point corresponding to a finite temperature where the dephasing time diverges. This fixed point can be associated with a toy version of 2D ergodic-to-MBL transition, provided that it survives to ε=2.

Mar 9, 20180 citations

Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping

Matthew S. Foster, Andreas W. W. Ludwig

We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in $d=3$ spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an $ϵ$ expansion in $d=2+ϵ$ dimensions. We find that in $d=2$ dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in $d>2$ dimensions $(ϵ>0)$ occurs for disorder strengths of order $ϵ$ , and is therefore perturbatively accessible for $ϵ⪡1$ . We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in $d=3$ spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an $ϵ$ expansion in $d=2+ϵ$ dimensions. We find that in $d=2$ dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in $d>2$ dimensions $(ϵ>0)$ occurs for disorder strengths of order $ϵ$, and is therefore perturbatively accessible for $ϵ⪡1$. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.

arXiv:0710.0400Physical Review BApr 3, 200837 citations

Beta‐functions of non‐linear σ‐models for disordered and interacting electron systems

Luca Dell’Anna

We provide and study complete sets of one‐loop renormalization group equations of several Finkel'stein non‐linear σ models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors. imageWe provide and study complete sets of one‐loop renormalization group equations of several Finkel'stein non‐linear σ models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors. image

arXiv:1610.05691Annalen der PhysikFeb 28, 20174 citations

Slow dynamics and ergodicity breaking in many-body systems

Federico Balducci

Sep 12, 20220 citations

d=3

spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an

ϵ

expansion in

d=2+ϵ

dimensions. We find that in

d=2

dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in

d>2

dimensions

(ϵ>0)

occurs for disorder strengths of order

ϵ

, and is therefore perturbatively accessible for

ϵ⪡1

. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.