The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS).TCI learns a compact MPS representation of the entire object from a tiny training data set. We will introduce a new open-source implementation of TCI: xfac/TCI.jl [1]. We will briefly introduce improved TCI algorithms and...
Since its original proposal [1], the existence and microscopic realization of deconfined quantum critical (DQC) points with lattice models has been under extensive debate. Field-theoretic arguments for DQC provide a plausible scenario where the quantum phase transition between a Neel phase and a valence-bond solid phase -- two most basic phases of matter in quantum magnetism -- will...
Entanglement measures provide powerful tools for diagnosing quantum many-body phases of matter. In particular, in (1+1)-dimensional systems with conformal symmetry, entanglement entropy exhibits logarithmic scaling, where the coefficient determines the central charge of the underlying conformal field theory (CFT). However, in the absence of the unitary condition, the central charge can be...
Simulating the real or imaginary time evolution of a quantum state using tensor networks requires constructing a representation of the time evolution operator, which can only be done approximately (except in some trivial cases). As an alternative to the common Trotter-Suzuki decomposition, we construct directly a Matrix Product Operator representation of the exponential function[1], which has...
The presence of athermal high-energy eigenstates in quantum many-body systems, known as quantum many-body scars, challenges the Eigenstate Thermalization Hypothesis. This article introduces a formulation of quantum many-body scars (QMBS) by interpreting the many-body Hilbert space as a Fock space graph, with a focus on closed quantum systems with weak ergodicity breaking. In this framework,...
