Abstract We investigate the entanglement in Hubbard models of hardcore bosons in 1 D , with an additional hardcore interaction on nearest-neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor 1/2 due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.
We introduce a systematic framework for calculating the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a non-interacting fermion system. We show that when working with a finite number of particles N , the Rényi entanglement entropies grow as ln N , with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite size scaling forms of the corrections to the scaling.
Many-body phenomena were always an integral part of physics comprising of collective behaviors through self-organization, in systems consisting of many components and degrees of freedom. We investigate the collective behaviors of strongly interacting particles confined in one dimension. We show that many-body orders with topological characteristics can be found at the Mott insulator limit for hardcore bosons, at different fillings, without considering the spin degree of freedom or long-range microscopic interactions. These orders have unique properties like weak or strong quantum correlations (entanglement), quantified by the entanglement entropy, edge excitations/modes and gapped energy spectrum with highly degenerate ground state, bearing resemblance to topologically ordered phases of matter.
The area law relates the bipartite entanglement entropy of a quantum many-body ground state to the size of the boundary between the subsystems, but the geometry of this boundary is rarely discussed. We inspect this in the 1D Bose-Hubbard model at fixed density by comparing four spatial bipartitions of the periodic lattice: first half, second half, even sites, and odd sites; sharing the same number of sites but differing in how the boundary is arranged. We find analytical limits with perturbation theory: in the Mott insulator the contiguous cut obeys the area lay while the alternating cut obeys a volume law
S∝Ns, in this sense an anomaly, and for the superfluid both cuts colapse to the binomial saturation due to delocalization of the state. We formulate these limits as a statement about the many-body problem using a generalized slave-boson approach based on mean-field with quantum fluctuations while verifying with Exact Diagonalization (ED) for small lattice sizes and Densitiy Matrix Renormalization Group (DMRG) simulations for
Ns≫1. The slave-boson Gaussian ground state allows to compute the entanglement entropy from a reduced correlation matrix for any desired bipartition consistent with ED and DMRG results. Using slave bosons the computational cost is set by the local cutoff
nmax rather than the Hilbert space dimension, so we can reach lattice sizes far beyond ED. Our method is capable of establishing the partition-dependent scaling laws as a many-body feature, not only a finite-size effect, in great agreement with the ED for
Ns∈[4,10] and DMRG for larger lattice sizes.
The entanglement in a Hubbard chain of hardcore bosons is investigated. The analytic expression of the global entanglement in the ground state is derived. The divergence of the derivative of the global entanglement shows the quantum criticality of the ground state. For the thermal equilibrium state, the bipartite and the multipartite entanglement are evaluated. The entanglement decreases to zero at a certain temperature. The thermal entanglement is rapidly decreasing with the increase of the number of sites in the lattice. The bipartite thermal entanglement approaches a constant value at a certain number of sites while the multipartite entanglement eventually vanishes.
We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N, the Rényi entanglement entropies grow as lnN, with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling. ar
Understanding what limits many-body quantum entanglement is a central problem in physics. Spatial locality has long provided a fundamental mechanism: correlations between a region and its complement must be mediated through a small spatial interface, thereby constraining their entanglement. Here we show that universal constraints on entanglement can persist even when interactions are strongly nonlocal, through collectivity: many weak interactions generate fluctuations controlled by their square-summed, rather than total, strength. We establish this mechanism rigorously for generic gapped Hamiltonians with Kac-normalized power-law interactions
r−α on a
D-dimensional lattice. For arbitrary bipartitions, we prove that the ground-state entanglement scales at most logarithmically with system size for
α<D/2 and subextensively for
D/2<α<D, due to suppressed collective fluctuations around individual sites. For spatially regular bipartitions with codimension-one boundaries, we use a renormalization-group construction to extend this suppression to larger length scales, yielding polylogarithmic scaling for
D/2<α<(D+1)/2 and parametrically stronger subvolume bounds for
(D+1)/2<α<D. We also establish the corresponding optimality results: for arbitrary bipartitions, the logarithmic scaling for
α<D/2 is optimal and
α=D/2 marks the optimal threshold for universal logarithmic bounds, while for regular bipartitions the threshold at
α=(D+1)/2 is likewise optimal for universal polylogarithmic bounds when
D≥2. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.