The Effects of Quantum Delocalization on the Structural and Thermodynamic Properties of Many-Body Systems

Andrew C. Potter, Romain Vasseur, S. A. Parameswaran

Developments in ultracold atomic experimental techniques highlight fundamental questions of whether quantum systems obey thermodynamics and statistical mechanics when isolated from their environment. A numerical technique is used to study phase transitions between thermal quantum fluids that obey thermodynamics and frozen quantum glasses that do not.

Winton Brown, Dhrubo Jyoti, Lorenza Viola

Masahito Ueda

Xu Feng, Shu Chen

The skin effect, characterized by the tendency of particles to accumulate at the boundaries, has been extensively studied in non-Hermitian systems. In this paper, we propose an intuitive Lindbladian composed of two chains with reversed skin localization. The skin steady state is gradually delocalized as the interchain coupling increases. In the single-body scenario, it corresponds to a shift in the scaling of the Liouvillian gap $\mathrm{\ensuremath{\Delta}}$ from $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{0}$ to $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{\ensuremath{-}2}$. Notably, exact diagonalization results reveal a system-size sensitivity of the single-particle Liouvillian spectrum, inherited from the system-size sensitivity of the non-Hermitian effective Hamiltonian. We predict that even an arbitrarily small coupling will induce dramatic changes in the Liouvillian spectrum and steady state in the thermodynamic limit, a phenomenon we term the critical Liouvillian skin effect. Additionally, in the many-body scenario, by employing the stochastic Schr\"odinger equation to unravel the Lindblad master equation, it is revealed that the scaling behavior of steady-state entanglement changes from the area law to the logarithmic law. In this paper, we demonstrate the delocalization of both single- and many-body skin steady states, introducing a mechanism for inducing entanglement transitions beyond the quantum Zeno effect.

C. Stephen Hellberg

Geneviève Fleury, Xavier Waintal

Using a combination of ground state quantum Monte Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localization length of a disordered two-dimensional electron gas. We find that correlations delocalize the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalization is much more dramatic in the presence of valley degeneracy [as in Si metal-oxide-semiconductor field-effect transistors], where the localization length increases drastically. We find that a simple mechanism accounts for the main features of the metallic behavior observed in two-dimensional gases. Our findings support the claim that this behavior is a genuine effect of the presence of interactions, yet that the system is not a "true" metal in the thermodynamic sense.