Related papers: Gaplessness is not generic for translation-invaria…
We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass-paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the…
We analytically study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical XXZ spin-half chains using field theoretical methods. When the system is gapped, the momentum-space entanglement Hamiltonian…
While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four…
For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one…
Sampling all ground states of a Hamiltonian with equal probability is a desired feature of a sampling algorithm, but recent studies indicate that common variants of transverse field quantum annealing sample the ground state subspace…
In this exposition we investigate further the general methodology proposed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain $\cla=\otimes_{\IZ}M_d$,…
We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-$\tfrac{1}{2}$ chains. The effect of the localised perturbation does not fade away however large the…
Pick a formal system. Any formal system. Whatever your favourite formal system is, as long as it's capable of reasoning about elementary arithmetic. The First Spectral Gap Incompleteness Theorem of [CPGW15] proved that there exist…
Motzkin spin-chains, which include 'colorless' (integer spin $s=1$) and 'colorful' ($s \geq 2$) variants, are one-dimensional (1D) local integer spin models notable for their lack of a conformal field theory (CFT) description of their…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current…
S=1/2 quantum spin chains and ladders with random exchange coupling are studied by using an effective low-energy field theory and transfer matrix methods. Effects of the nonlocal correlations of exchange couplings are investigated…
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap $\epsilon$ has correlation length $\xi$ upper bounded as…
It is shown that every one-dimensional Hamiltonian with short-range interaction admits a quantum Gibbs sampler [CKG23] with a system-size independent spectral gap at all finite temperatures. Consequently, their Gibbs states can be prepared…
Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any…
We investigate quantum phase transitions in which a change in the type of entanglement from bound entanglement to either free entanglement or separability may occur. In particular, we present a theoretical method to construct a class of…
Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise…
Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…
Using rigorous analytical analysis and exact numerical data for the spin-1/2 transverse Ising chain we discuss the effects of regular alternation of the Hamiltonian parameters on the quantum phase transition inherent in the model.
An interesting feature of spin-1/2 chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field $H$. The system is in a gapless incommensurate regime for all values of the…