In this paper we calculate the block entanglement entropies of spin models whose ground states have perfect antiferromagnetic or ferromagnetic long-range order. In the latter case the definition of entanglement entropy is extended to properly take into account the ground state degeneracy. We find in both cases the entropy grows logarithmically with the block size. Implication of our results on states with general long-range order will be discussed.
We show that spatial resolved dissipation can act on Ising lattices molding the universality class of their critical points. We consider non-local spin losses with a Liouvillian gap closing at small momenta as $propto q^alpha$, with $alpha$ a positiv
e tunable exponent, directly related to the power-law decay of the spatial profile of losses at long distances. The associated quantum noise spectrum is gapless in the infrared and it yields a class of soft modes asymptotically decoupled from dissipation at small momenta. These modes are responsible for the emergence of a critical scaling regime which can be regarded as the non-unitary analogue of the universality class of long-range interacting Ising models. In particular, for $0<alpha<1$ we find a non-equilibrium critical point ruled by a dynamical field theory ascribable to a Langevin model with coexisting inertial ($proptoomega^2$) and frictional ($proptoomega$) kinetic coefficients, and driven by a gapless Markovian noise with variance $propto q^alpha$ at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Furthermore, by employing a one-loop improved RG calculation, we estimate the conditions for observability of this scaling regime before incoherent local emission intrudes in the spin sample, dragging the system into a thermal fixed point. We also explore other instances of criticality which emerge for $alpha>1$ or adding long-range spin interactions. Our work lays out perspectives for a revision of universality in driven-open systems by employing dark states supported by non-local dissipation.
We investigate the thermal and transport properties of CexLa1-xRu2Al10 to clarify the origin of the recently discovered mysterious phase below T0=27 K in CeRu2Al10 where a large magnetic entropy is released, however, the existence of an internal magn
etic field is ruled out by 27Al-NQR measurement. We find that T0 decreases with decreasing x and disappears at x~0.45. T0 of CeRu2Al10 is suppressed down to 26 K under H=14.5 T along the a-axis. These results clearly indicate that the transition has a magnetic origin and is ascribed to the interaction between Ce ions. Considering the results of specific heat, magnetic susceptibility, thermal expansion, and electrical resistivity and also 27Al NQR, we propose that the transition originates from the singlet pair formation between Ce ions. Although its properties in a Ce dilute region is basically understood by the impurity Kondo effect, CeRu2Al10 shows a Kondo-semiconductor-like behavior. The phase transition at T0 may be characterized as a new type of phase transition that appears during the crossover from the dilute Kondo to the Kondo semiconductor.
We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time
crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical $n$-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.
We consider the entanglement between two spatial subregions in the Lieb-Liniger model of bosons in one spatial dimension interacting via a contact interaction. Using ground state path integral quantum Monte Carlo we numerically compute the R{e}nyi en
tropy of the reduced density matrix of the subsystem as a measure of entanglement. Our numerical algorithm is based on a replica method previously introduced by the authors, which we extend to efficiently study the entanglement of spatial subsystems of itinerant bosons. We confirm a logarithmic scaling of the R{e}nyi entropy with subsystem size that is expected from conformal field theory, and compute the non-universal subleading constant for interaction strengths ranging over two orders of magnitude. In the strongly interacting limit, we find agreement with the known free fermion result.
In this short note we discuss the relation between the so-called Off-Diagonal-Long-Range-Order in many-body interacting quantum systems introduced by C. N. Yang in Rev. Mod. Phys. {bf 34}, 694 (1962) and entanglement. We argue that there is a direct relation between these two concepts.