相关论文: Tensor Networks: Phase transition phenomena on hyp…

A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…

Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in…

Technological and scientific advances have given rise to an era in which coherent quantum-mechanical phenomena can be probed and experimentally-realised over unprecedented timescales in condensed matter physics. In turn, scientific interest…

The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have…

The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives.…

Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By…

We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…

In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for…

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…

Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and…

The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it is used to describe graphene predicting a quantum phase transition from a semimetal to a…

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

Complex quantum systems are often multiscale in nature with strong interactions between different scales. We present a novel idea: iteratively suppressing, rather than tracing out, the fast, high-energy degrees of freedom in strongly…