Related papers: Gaplessness is not generic for translation-invaria…
We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high `entanglement energy' levels, from a flat band of levels with specific…
New effects in the frustrated transverse Ising ring are predicted. The system is solved based on a mapping of Pauli spin operators to the Jordan-Wigner fermions. We group the low-lying energy levels into bands after imposing appropriate…
Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
Given a direct system of Hilbert spaces $s\mapsto \mathcal H_s$ (with isometric inclusion maps $\iota_s^t:\mathcal H_s\rightarrow \mathcal H_t$ for $s\leq t$) corresponding to quantum systems on scales $s$, we define notions of scale…
We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the…
We consider general locally-interacting arbitrary-dimensional lattice spin systems that are gapped for any system size. We show under reasonable conditions that nondegenerate ground states of such systems obey the entanglement area law. In…
In this paper we report the latest results of exact diagonalizations of SU(2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagome lattices). We focus on the low lying levels in each S sector. The…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
Designing a good transfer channel for arbitrary quantum states in spin chains implies optimizing a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles…
While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a…
We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors…
We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground…
This paper concerns the problem of non-ideal state transfer along the alternating open chain of spins $s=1/2$ with XY Hamiltonian. It is found that the state transfer along the chain with even number of spins $N$ ($N=4,6,8$) may be realized…
We examine a chain of periodic arrays of 4 quantum spins with magnitudes of 1/2, 1, 3/2 and 1. There are four kinds of nearest-neighbour exchange parameters among them. We choose two independent parameters for concreteness: one represents…
We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal…
We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these…
Motivated by the $\Omega$-spectrum proposal of unique gapped ground states by Kitaev, we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial…
In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of…
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional…