相关论文: Improved bounds on the spectral gap above frustrat…
We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…
We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-1/2 chain with diagonal boundary magnetic fields in the noncritical regime (Delta > 1). Our result, which is formulated in terms of q-gamma…
We develop a boundary field theory approach to electron spin resonance in open $S=1/2$ Heisenberg antiferromagnetic chains with an effective staggered field. In terms of the sine Gordon effective field theory with boundaries,we point out…
A fundamental question is understanding the rate at which random quantum circuits converge to the Haar measure. One quantity which is important in establishing this rate is the spectral gap of a random quantum ensemble. In this work we…
Haldane's seminal work established two fundamentally different types of excitation spectra for antiferromagnetic Heisenberg quantum spin chains: gapped excitations in integer-spin chains and gapless excitations in half-integer-spin chains.…
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe…
We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…
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…
The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases…
A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock,…
Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap…
Establishing the (non)existence of a spectral gap above the ground state in the thermodynamic limit is one of the fundamental steps for characterizing the topological phase of a quantum lattice model. This is particularly challenging when a…
We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…
We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit $\Delta\to\infty$. Near the isotropic point, $\Delta=1$, the estimates are good…
We apply Witten's conjugation argument [Nucl. Phys. B 202, 253 (1982)] to spin chains, where it allows us to derive frustration-free systems and their exact ground states from known results. We particularly focus on $\mathbb{Z}_p$-symmetric…
A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion of curvature of the diffusion, like the coarse Ricci…
We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with general integrable boundary terms (containing six free boundary parameters) at roots of unity. We use this solution, together with an…
Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed. We use these solutions to compute the…
Various constraints concerning control fields can be imposed in the realistic implementations of quantum control systems. One of the most important is the restriction on the frequency spectrum of acceptable control parameters. It is…
A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based…