We introduce a unary coding of bosonic occupation states based on the famous balls and walls counting for the number of configurations of $N$ indistinguishable particles on $L$ distinguishable sites. Each state is represented by an integer with a hum
an readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order $L$ over current methods when generating the basis states of bosonic lattice models. The unary coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to $L=N=20$, and the time needed to generate the ground state block is reduced to a fraction of the diagonalization time. For the ground state symmetry resolved entanglement, we demonstrate that variational approaches restricting the local bosonic Hilbert space could result in an error that scales with system size.
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functio
ns, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.
We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of the steady state entanglement entropy density under either a spatial mode or particle bipartition. For integrable lattice models, we find excelle
nt agreement between the increase of spatial and particle entanglement entropy, and for chaotic models, an examination of two further neighbor interaction strengths suggests similar correspondence. This result highlights the generality of the dynamical conversion of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics.
For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is
inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and
Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Renyi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to $10^5$ particles.
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental conditions,
i.e., temporal disorder. Using large-scale Monte-Carlo simulations of up to $3times 10^7$ organisms and $10^5$ generations, we find the extinction transition in time-independent environments to be in the well-known directed percolation universality class. In contrast, temporal disorder leads to a highly unusual extinction transition characterized by logarithmically slow population decay and enormous fluctuations even for large populations. The simulations provide strong evidence for this transition to be of exotic infinite-noise type, as recently predicted by a renormalization group theory. The transition is accompanied by temporal Griffiths phases featuring a power-law dependence of the life time on the population size.
We investigate the scaling of the R{e}nyi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second R{e}nyi entanglement entropy and s
how that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional $t-V$ model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.
We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulat
ions in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.
We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such random-field disorder destroys the phas
e transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.
We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally in the act
ive phase while the bulk system is still in the inactive phase. Specifically, if the correlations decay as a power of the distance, the rare region probability is a stretched exponential of the rare region size rather than a simple exponential as is the case for uncorrelated disorder. As a result, the Griffiths singularities are enhanced and take a non-power-law form. The critical point itself is of infinite-randomness type but with critical exponent values that differ from the uncorrelated case. We report large-scale Monte-Carlo simulations that verify and illustrate our theory. We also discuss generalizations to higher dimensions and applications to other systems such as the random transverse-field Ising model, itinerant magnets and the superconductor-metal transition.
