Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds

We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.

The mass scales of the Higgs field

In the first version of the theory, with a classical scalar potential, the sector inducing SSB was distinct from the Higgs field interactions induced through its gauge and Yukawa couplings. We have adopted a similar perspective but, following most recent lattice simulations, described SSB in [Formula: see text] theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: (i) a lower mass [Formula: see text], defined by its quadratic shape at the minima, and (ii) a larger mass [Formula: see text], defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by [Formula: see text], where [Formula: see text] is the ultraviolet cutoff of the scalar sector. We have checked this two-scale structure with lattice simulations of the propagator and of the susceptibility in the 4D Ising limit of the theory. These indicate that, in a cutoff theory where both [Formula: see text] and [Formula: see text] are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. [Formula: see text] GeV, to a much larger [Formula: see text]. The same lattice data give a final estimate [Formula: see text] GeV which induces to reconsider the experimental situation at Large Hadron Collider (LHC). In particular an independent analysis of the ATLAS[Formula: see text]+[Formula: see text]CMS data indicating an excess in the 4-lepton channel as if there were a new scalar resonance around 700 GeV. Finally, the presence of two vastly different mass scales, requiring an interpolating form for the Higgs field propagator also in loop corrections, could reduce the discrepancy with those precise measurements which still favor large values of the Higgs particle mass.

Mobility of spin polarons with vertex corrections

The mobility of holes in the spin polaron theory is discussed in this paper using a representation where holes are described as spinless fermions and spins as normal bosons. The hard-core bosonic operator is introduced through the Holstein–Primakoff transformation. Mathematically, the theory is implemented in the finite temperature (Matsubara) Green’s function method. The expressions for the zeroth-order term of the hole mobility is determined explicitly for hole occupation factor taking the form of Fermi–Dirac distribution and the classical Maxwell–Boltzmann distribution function. These are proportional to the relaxation time and the square of the renormalization factor. In the Ising limit, we showed that the mobility is zero and the holes are localized. The calculation of the hole mobility is generalized by considering the vertex corrections, which included the ladder diagrams. One of the vertex functions in the hole mobility can be evaluated using the Ward identity for hole-spin wave weak interaction. We also derived an expression for the hole mobility with vertex corrections in the low-temperature limit and vanishing self-energy effects. Our calculation is made up to second-order correction in the case where the hole occupation factor follows the Fermi–Dirac distribution.

Corrections to finite-size scaling in the φ4 model on square lattices

Corrections to scaling in the two-dimensional (2D) scalar [Formula: see text] model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L ([Formula: see text]) and different values of the [Formula: see text] coupling constant [Formula: see text], i.e. [Formula: see text], 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction–to–scaling exponents [Formula: see text] become small when approaching the Ising limit ([Formula: see text]), but such corrections generally exist in the 2D [Formula: see text] model. Analytical arguments show the existence of corrections with the exponent [Formula: see text]. The numerical analysis suggests that there exist also corrections with the exponent [Formula: see text] and, perhaps, also with the exponent about [Formula: see text], which are detectable at [Formula: see text]. The numerical tests provide an evidence that the structure of corrections to scaling in the 2D [Formula: see text] model differs from the usually expected one in the 2D Ising model.

Ferrimagnetic order and spontaneous magnetization in a mixed-spin XXZ chain with single-ion anisotropy

The ground-state properties of the spin-(1/2, 1) mixed-spin XXZ chain with single-ion anisotropy (D) are investigated by the infinite time-evolving block decimation (iTEBD) method. A ground-state phase diagram including three phases, i.e., a fully polarized phase, an XY phase and a ferrimagnetic phase, is obtained. The ferrimagnetic phase is found to extend to the regions with (Δ > 1, D > 0) and (Δ < 1, D < 0), where Δ denotes the coupling anisotropy between the localized spins. By the discontinuous behavior of bipartite entanglement, quantum phase transitions (QPTs) between the XY phase and the other two phases are verified to be of the first-order. Furthermore, two constant spontaneous magnetization values (Mz = 3/2 and 1/2) are observed in the fully polarized and the ferrimagnetic phases, respectively. In both cases of Δ → +∞ and D → -∞, the ground state tends to the Ising limit. In addition, both the long-range ferromagnetic and antiferromagnetic orders are found to coexist in the whole ferrimagnetic phase.

ON THE LOW-ENERGY SPECTRUM OF SPONTANEOUSLY BROKEN Φ4THEORIES

The low-energy spectrum of a one-component, spontaneously broken Φ4theory is generally believed to have the same simple massive form [Formula: see text] as in the symmetric phase where 〈Φ〉 = 0. However, in lattice simulations of the 4D Ising limit of the theory, the two-point connected correlator and the connected scalar propagator show deviations from a standard massive behavior that do not exist in the symmetric phase. As a support for this observed discrepancy, we present a variational, analytic calculation of the energy spectrum E1(p) in the broken phase. This analytic result, while providing the trend [Formula: see text] at large |p|, gives an energy gap E1(0)< mh, even when approaching the infinite-cutoff limit Λ→∞ with that infinitesimal coupling λ ~ 1/ ln Λ suggested by the standard interpretation of "triviality" within leading-order perturbation theory. We also compare with other approaches and discuss the more general implications of the result.

ENTANGLEMENT IN THE ANISOTROPIC KONDO NECKLACE MODEL

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.