相关论文: Renormalisation and fixed points in Hilbert Space

The low-lying bound states of a microscopic quantum many-body system of $n$ particles and the related physical observables can be worked out in a truncated $n$--particle Hilbert space. We present here a non-perturbative analysis of this…

We propose and test a renormalization procedure which acts in Hilbert space. We test its efficiency on strongly correlated quantum spin systems by working out and analyzing the low-energy spectral properties of frustrated quantum spin…

Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave…

We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly…

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…

Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation.…

We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided…

We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in…

We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction…

We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…

Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…

We study a simple and tractable model of many-body localization. The main idea is to take a renormalization group perspective in which local entanglement is removed to reach a product state. The model is built from a random local unitary…

Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…

For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the…

Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in {\it e.g.}…

Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the…

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…

We study the regularization and renormalization of a finite range inverse cube potential in the two- and three-body sectors. Specifically, we compare and contrast three different regulation schemes frequently used to study few-body systems…

We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through…