We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c = 1 bosonic field theory. A numerical analysis of a spin-chain model reveals that the mutual information is scale-invariant and depends directly on the boson radius. We interpret the results in terms of correlation functions of branch-point twist fields. The present study provides a new way to determine the boson radius, and furthermore demonstrates the power of the mutual information to extract more refined information of conformal field theory than the central charge. Given a microscopic model, an important and often nontrivial issue is how to obtain the effective field theory controlling its long-distance behavior. The notion of quantum entanglement, or more specifically, the entanglement entropy, has been extensively applied as a new way to address this basic matter. From a quantum ground state |Ψ , one constructs the reduced density matrix ρ A := TrĀ |Ψ Ψ| on a subsystem A by tracing out the exteriorĀ. The entanglement entropy is defined as S A := −Tr ρ A log ρ A . In 1D quantum critical systems, the entanglement entropy for an interval A = [x 1 , x 2 ] embedded in a chain exhibits a universal scaling [6,7,8,9,10,11]:where c is the central charge of the CFT and s 1 is a nonuniversal constant related to the ultra-violet (UV) cutoff. This scaling allows to determine the universal number c as a representative of the ground state structure, without having to worry about the precise correspondence between the microscopic model and the field theory.As it is well known, the central charge is not the only important number specifying a CFT. In the bosonic field theory with c = 1, the boson compactification radius R (or equivalently, the TLL parameter K = 1/(4πR 2 )) is a dimensionless parameter which changes continuously in a phase and controls the power-law behavior of various physical quantities. It is natural to ask how to identify the boson radius as a generic structure of the ground state. In this Letter, we demonstrate that the entanglement entropy can achieve this task if we consider two disjoint intervals, A = [x 1 , x 2 ] and B = [x 3 , x 4 ]. We analyze the scaling of the mutual information defined asThis measures the amount of information shared by two subsystems [12,13]. A numerical analysis of a spin-chain model reveals a robust relation between I A:B and R, irrespective of microscopic details. We compare the result with the general prediction of Calabrese and Cardy (CC) [9], and find a relevant correction to their result. Roughly speaking, the mutual information (2) may be regarded as a region-region correlator. It is known that I A:B is non-negative, and becomes zero iff ρ A∪B = ρ A ⊗ ρ B , i.e., in a situation of no correlation [14]. A motivation to consider I A:B comes from that microscopic details at short-range scales, which are often obstacles when analyzing point-point correlators, can be smoothed out over regions. As we enlar...

International audienceWe study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S_0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S_0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S_0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point

Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii–Kosterlitz–Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

Ones and twos: The two‐photon absorption cross sections (σ(2)) of singlet diradical hydrocarbons with phenalenyl peripheral groups (see scheme) are larger than those of closed‐shell aromatic hydrocarbons by an order of magnitude or more and are comparable to those of π‐conjugated compounds with strong electron donor or acceptor substituents. A significant increase in cross section was also observed in the resonance‐enhanced region.

The ground-state phase diagram of a spin-1 2 XXZ chain with competing ferromagnetic nearestneighbor (J1 < 0) and antiferromagnetic second-neighbor (J2 > 0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range −4 < J1/J2 < 0 has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and Néel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and Néel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.