Related papers: The Non-Abelian Density Matrix Renormalization Gro…
We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we…
A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians,…
A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…
In this paper we study a renormalization-group map: the block averaging transformation applied to Gibbs measures relative to a class of finite range lattice gases, when suitable strong mixing conditions are satisfied. Using block decimation…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
The infinite Density Matrix Renormalisation Group (iDMRG) algorithm is a highly successful numerical algorithm for the study of low-dimensional quantum systems, and is also frequently used to initialise the more popular finite DMRG…
A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes…
The phenomenon of degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(\lambda)$ the degeneracy occurs at a Kato's exceptional point…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
A new block spin renormalization group transformation for SU(N) gauge models is proposed near the non-trivial fixed point in perturbation theory and thereby the expectation values of various Wilson loops on the renormalized trajectory near…
We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. $R$-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval.…
We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of…
The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…