Related papers: Solving frustration-free spin systems
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of…
Let $H$ be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions, a unique ground state, and local spectral gap lower bounded by a positive constant. For any bipartition defined by a vertical cut of length…
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and…
Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…
We study frustrated quantum systems from a quantum information perspective. Within this approach, we find that highly frustrated systems do not follow any general ''area law'' of block entanglement, while weakly frustrated ones have area…
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum…
We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…
We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical…
We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the {ground state of our model is non-degenerate and exhibits} a novel quantum phase transition from bounded entanglement…
Many-body localization was proven under realistic assumptions by constructing a quasi-local unitary rotation that diagonalizes the Hamiltonian (Imbrie, 2016). A natural generalization is to consider all unitaries that have a similar…
Frustration is a ubiquitous phenomenon in many-body physics that influences the nature of the system in a profound way with exotic emergent behavior. Despite its long research history, the analytical or numerical investigations on…
We present a class of exactly solvable 2D models whose ground states violate conventional beliefs about entanglement scaling in quantum matter. These beliefs are (i) that area law entanglement scaling originates from local correlations…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the…