Weak Eigenstate Research Articles

Normal weak eigenstate thermalization

Normal weak eigenstate thermalization

Quantum Concentration Inequalities

We establish Transportation Cost Inequalities (TCIs) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: First, we generalize the Dobrushin uniqueness condition to prove that Gibbs states of 1D commuting Hamiltonians satisfy a TCI at any positive temperature and provide conditions under which this first result can be extended to non-commuting Hamiltonians. Next, using a non-commutative version of Ollivier’s coarse Ricci curvature, we prove that high temperature Gibbs states of commuting Hamiltonians on arbitrary hypergraphs H=(V,E) satisfy a TCI with constant scaling as O(|V|). Third, we argue that the temperature range for which the TCI holds can be enlarged by relating it to recently established modified logarithmic Sobolev inequalities. Fourth, we prove that the inequality still holds for fixed points of arbitrary reversible local quantum Markov semigroups on regular lattices, albeit with slightly worsened constants, under a seemingly weaker condition of local indistinguishability of the fixed points. Finally, we use our framework to prove Gaussian concentration bounds for the distribution of eigenvalues of quasi-local observables and argue the usefulness of the TCI in proving the equivalence of the canonical and microcanonical ensembles and an exponential improvement over the weak Eigenstate Thermalization Hypothesis.

Flavor specific [formula omitted] gauge model for muon g − 2 and [formula omitted] anomalies

The muon (g−2)μ and b→sμ¯μ induced B anomalies as hints of new physics beyond the standard model (SM) have attracted much attention. These two anomalies indicate that there may exist new interaction specifically related to muon. A lot of theoretical ideas have been proposed to explain these anomalies. Gauged flavor specific U(1)Bq−Lμ is among the promising ones. The new gauge boson Z′ from U(1)Bq−Lμ interacts with muon and provides necessary ingredient to solve the (g−2)μ anomaly. The Z′-quark coupling can generate flavor changing interactions after diagonalization of quark mass matrix between weak eigen-state and mass eigen-state basis. We revisit challenges for such models attempting to explain the (g−2)μ and B anomalies separately or simultaneously. We find although for U(1)Bq−Lμ models there is still parameter space to provide solutions for separately explaining the (g−2)μ and B anomalies, there exists no parameter space for such models to solve both the anomalies simultaneously, after taking into account existing constraints from τ→μγ, τ→3μ, neutrino trident and Bs−B¯s data. Among them leptonic processes restrict Z′ mass to be less than a few hundred MeV if required to solve the (g−2)μ anomaly, which causes conflict between data from Bs−B¯s, D0−D¯0 mixing and also hadron decays with Z′ in the final states. The effects of U(1)Y and U(1)Bq−Lμ kinetic mixing on these anomalies are also studied. We find that neither can these effects do much to bring the two anomalies together to be solved simultaneously.

Eigenstate entanglement scaling for critical interacting spin chains

With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.

Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interactions

This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body observables is restricted by a Gaussian concentration bound (or Chernoff–Hoeffding inequality) above some threshold temperature. This bound is then derived for arbitrary Gibbs states of systems that include long-range interactions Secondly, we establish a quantitative relationship between the concentration bound of the Gibbs state and the equivalence of canonical and micro-canonical ensembles. We then evaluate the difference in the averages of thermodynamic properties between the canonical and the micro-canonical ensembles. Under the assumption of the Gaussian concentration bound on the canonical ensemble, the difference between the ensemble descriptions is upper-bounded by n−1log(n3∕2Δ−1)1∕2 with n being the system size and Δ being the width of the energy shell of the micro-canonical ensemble This limit gives a non-trivial upper bound exponentially small energy width with respect to the system size. By combining these two results, we prove the ensemble equivalence as well as the weak eigenstate thermalization in arbitrary long-range-interacting systems above a threshold temperature.

Dynamical Typicality Approach to Eigenstate Thermalization.

We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit an arbitrary but fixed nonequilibrium expectation value for some given observable A. On the condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of A spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of A.

Study of Dirac fermionic dark matter

We study pure weak eigenstate Dirac fermionic dark matter (DM). We consider WIMP with renormalizable interaction. According to results of direct searches and the nature of DM (electrical neutral and being a pure weak eigenstate), the quantum number of DM is determined to be ${I}_{3}=Y=0$. There are only two possible cases: either DM has nonvanishing weak isospin ($I\ensuremath{\ne}0$) or it is an isosinglet ($I=0$). In the first case, the Sommerfeld enhancement is sizable for large $I$, producing large ${\ensuremath{\chi}}^{0}\overline{{\ensuremath{\chi}}^{0}}\ensuremath{\rightarrow}VV$ rates. In particular, we obtain large $\ensuremath{\chi}\overline{\ensuremath{\chi}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}$ cross section, which is comparable to the latest bounds from indirect searches and ${m}_{\ensuremath{\chi}}$ is constrained to be larger than a few hundred GeV to a few TeV. It is possible to give correct relic density with ${m}_{\ensuremath{\chi}}$ higher than these lower bounds. In the second case, to couple DM to standard model (SM) particles, a SM-singlet vector mediator $X$ is required from renormalizability and the SM gauge quantum numbers. To satisfy the latest bounds of direct searches and to reproduce the DM relic density at the same time, resonant enhancement in DM annihilation diagram is needed. Thus, the masses of DM and the mediator are related. Furthermore, this model is not sufficient to explain the deviation in muon $g\ensuremath{-}2$.

An alternative Yukawa unified SUSY scenario

Supersymmetric SO(10) Grand Unified Theories with Yukawa unification represent an appealing possibility for physics beyond the Standard Model. However Yukawa unification is made difficult by large threshold corrections to the bottom mass. Generally one is led to consider models where the sfermion masses are large in order to suppress these corrections. Here we present another possibility, in which the top and bottom GUT scale Yukawa couplings are equal to a component of the charged lepton Yukawa matrix at the GUT scale in a basis where this matrix is not diagonal. Physically, this weak eigenstate Yukawa unification scenario corresponds to the case where the charged leptons that are in the 16 of SO(10) containing the top and bottom quarks mix with their counterparts in another SO(10) multiplet. Diagonalizing the resulting Yukawa matrix introduces mixings in the neutrino sector. Specifically we find that for a large region of parameter space with relatively light sparticles, and which has not been ruled out by current LHC or other data, the mixing induced in the neutrino sector is such that $sin^2 2\Theta_{23} \approx 1$, in agreement with data. The phenomenological implications are analyzed in some detail.

Phenomenological minimal supersymmetric standard model dark matter searches on ice

We explore the capability of the IceCube/DeepCore array to discover signal neutrinos resulting from the annihilations of supersymmetric weakly interacting massive particles that may be captured in the solar core. In this analysis, we use a previously generated set of $\ensuremath{\sim}70\text{ }\text{ }\mathrm{k}$ model points in the 19-dimensional parameter space of the phenomenological minimal supersymmetric standard model (pMSSM) which satisfy existing experimental and theoretical constraints. Our calculations employ a realistic estimate of the IceCube/DeepCore effective area that has been modeled by the IceCube collaboration. We find that a large fraction of the pMSSM models are shown to have significant signal rates in the anticipated IceCube/DeepCore 1825 d data set, including some prospects for an early discovery. Many models where the lightest supersymmetric particle only constitutes a small fraction of the total dark matter relic density are found to have observable rates. We investigate in detail the dependence of the signal neutrino fluxes on the lightest-supersymmetric-particle mass, weak eigenstate composition, annihilation products and thermal relic density, as well as on the spin-independent and spin-dependent scattering cross sections. Lastly, we compare the model coverage of IceCube/DeepCore to that obtainable in near-future direct-detection experiments and to pMSSM searches at the 7 TeV LHC.

Proton decay and fermion masses in supersymmetric SO(10) model with unified Higgs sector

We make a detailed analysis of the proton decay in a supersymmetric SO(10) model proposed by K. Babu, I. Gogoladze, P. Nath, and R. Syed. We introduce quark mixing, and find that this model can generate fermion mass without breaking the experimental bound on proton decay. We also predict large Cabibbo-Kobayashi-Maskawa (CKM) unitarity violations. The CKM matrix $V$ in this paper is defined as normal, i.e. ${d}_{i}^{\ensuremath{'}}={V}^{ij}{d}_{j}$, where $ij$ run from 1 to 3. The primed field is the weak eigenstate and the unprimed field is the mass eigenstate.

Direct detection of the Wino and Higgsino-like neutralino dark matter at one-loop level

The neutralino-nucleon (\tilde{\chi}^0-N) scattering is an important process for direct dark matter searches. In this paper we discuss one-loop contributions to the cross section in the wino-like and Higgsino-like LSP cases. The neutralino-nucleon scattering mediated by the Higgs \tilde{\chi}^0\tilde{\chi}^0 and Z\tilde{\chi}^0\tilde{\chi}^0 couplings at tree level is suppressed by the gaugino-Higgsino mixing at tree level when the neutralino is close to a weak eigenstate. The one-loop contribution to the cross section, generated by the gauge interaction, is not suppressed by any SUSY particle mass or mixing in the wino- and Higgsino-like LSP cases. It may significantly alter the total cross section when \sigma_{\tilde{\chi}^0 N}\sim 10^{-45} cm^2 or less.

NEUTRINO OSCILLATIONS AND THE EXACT PARITY MODEL

We re-examine neutrino oscillations in exact parity models. Previously it was shown in a specific model that large neutrino mixing angles result. We show here that this is a general result of neutrino mixing in exact parity models provided that the neutrino mass matrix is real. In this case, the effects of neutrino mixing in exact parity models is such that the probability of a given weak eigenstate remaining in that eigenstate averages to less than half when averaged over many oscillations. This result is interesting in view of the accumulating evidence for a significant deficit in the number of solar neutrinos. It may also be of relevance to the atmospheric neutrino anomaly.

Possibility of observing massive neutrino admixtures in nuclear orbital electron capture rates.

The unusual case in nuclear orbital electron capture whereby either a neutrino in a weak interaction eigenstate or in a mass eigenstate is emitted by the same nucleus is examined. The case of the low-energy Q value nuclear electron capture decays is considered where, for at least one electronic shell, the emission of a weak eigenstate neutrino having an admixture of a second mass eigenstate neutrino (with mass in the keV/${\mathrm{c}}^{2}$ range) is energetically prohibited. This feature, in particular, opens the possibility for a new approach to searching for massive neutrino admixtures using relative electron capture rates. Five candidates are specifically identified, of which one, $^{157}\mathrm{Tb}$, is conceivably of immediate interest to the 17 keV/${\mathrm{c}}^{2}$ neutrino mass question. Finally experimental prospects and limitations are described.

CP restrictions on quark mass matrices

The general implications are studied of CP invariance on quark mass matrices within the standard SU(2) × U(1) gauge theory, with an arbitrary number of fermion families. In particular, a set of necessary conditions is derived for CP invariance that the quark mass matrices must satisfy when written in the weak eigenstate basis. These conditions are expressed in terms of traces of powers of the mass matrices. The violation of any of these conditions implies CP non-conservation by the charged current weak interactions. In the case of three generations, it is found that one of these conditions is also sufficient for CP invariance.

Search for Massive Neutrinos in the Decayπ→eν

The positron spectrum from the decay ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e}$ has been examined for evidence of peaks arising from an admixture in the ${\ensuremath{\nu}}_{e}$ weak eigenstate of massive neutrinos. Limits on the intensity of such peaks, together with the measured $\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\nu}$ branching ratio, have been used to derive constraints on the neutrino mixing parameters over the range $4 \mathrm{MeV}<m(\ensuremath{\nu})<135 \mathrm{MeV}$.