Related papers: Localization renormalization and quantum Hall syst…
We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate…
We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during…
We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-K\"ahler polarizations which occur generically on…
In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise. The regularizing norm in this scheme is stronger than the norm in Hilbert space. We focus on…
We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…
Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
A band with a nonzero Chern number cannot be fully localized by weak disorder. There must remain at least one extended state, which ``carries the Chern number.'' Here we show that a trivial band can behave in a similar way. Instead of fully…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
Chiral integer quantum Hall (QH) edge modes are immune to backscattering and therefore are non-localized and show a vanishing longitudinal as well as non-local resistance along with quantized 2-terminal and Hall resistance even in the…
Contractor renormalization (CORE) is a real-space renormalization-group method to derive effective Hamiltionians for microscopic models. The original CORE method is based on a real-space decomposition of the lattice into small blocks and…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
We investigate refined algebraic quantisation of the constrained Hamiltonian system introduced by Boulware as a simplified version of the Ashtekar-Horowitz model. The dimension of the physical Hilbert space is finite and asymptotes in the…
Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built…
We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
A superqubit, belonging to a $(2|1)$-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more nonlocal than ordinary qubits, we construct a…
We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping…
The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong…