Related papers: Symmetries and field tensor network states
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of…
Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum…
We prove that all eigenstates of many-body localized symmetry protected topological systems with time reversal symmetry have four-fold degenerate entanglement spectra in the thermodynamic limit. To that end, we employ unitary quantum…
Through coarse-graining, tensor network representations of a two-dimensional critical lattice model flow to a universal four-leg tensor, corresponding to a conformal field theory (CFT) fixed-point. We computed explicit elements of the…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…
Recently, it was realized that quantum states of matter can be classified as long-range entangled (LRE) states (i.e. with non-trivial topological order) and short-range entangled (SRE) states (\ie with trivial topological order). We can use…
Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However,…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
We study Gaussian continuous tensor network states (GCTNS) - a finitely-parameterized subclass of Gaussian states admitting an interpretation as continuum limits of discrete tensor network states. We show that, at short distance, GCTNS…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We introduce unitary network, an oriented architecture for tensor network unitaries. Compared to existing architectures, in a unitary network each local tensor is required to be a unitary matrix upon suitable reshaping. Global unitarity is…
Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…