118033851
A Lattice Non-Perturbative Hamiltonian Construction of 1+1D Anomaly-Free Chiral Fermions and Bosons - on the equivalence of the anomaly matching conditions and the boundary fully gapping rules
A non-perturbative Hamiltonian construction of chiral fermions and bosons with anomaly-free symmetry $G$ in 1+1D spacetime is proposed. More precisely, we ask "whether there is a local short-range finite quantum Hamiltonian system realizing onsite symmetry $G$ defined on a 1D spatial lattice with a continuous time, such that its low energy physics produces a 1+1D anomaly-free chiral matter theory of symmetry $G$?" Our answer is "yes." In particular, we show that the 3$_L$-5$_R$-4$_L$-0$_R$ U(1) chiral fermion theory, with two left-moving fermions of charge-3 and charge-4, and two right-moving fermions of charge-5 and charge-0 at low energy, can be put on a 1D spatial lattice where the U(1) symmetry is realized as an onsite symmetry, if we include properly-designed interactions between fermions with intermediate strength. We show how to design such proper interactions by looking for interaction terms with extra symmetries. In general, we show that any 1+1D U(1)-anomaly-free chiral matter theory can be defined as a finite system on 1D lattice with onsite symmetry, by using a quantum Hamiltonian with a continuous time, if we include properly-designed interactions between matter fields. We comment on the new ingredients and the differences of ours comparing to Eichten-Preskill and Chen-Giedt-Poppitz models, and suggest modifying Chen-Giedt-Poppitz model to have successful mirror-decoupling. As an additional remark, we show a topological non-perturbative proof on the equivalence relation between 't Hooft anomaly matching conditions and the boundary fully gapping rules of U(1) symmetry.
59494220
Symmetry-protected topological phases with charge and spin symmetries: Response theory and dynamical gauge theory in two and three dimensions
A large class of symmetry-protected topological phases (SPT) in boson / spin systems have been recently predicted by the group cohomology theory. In this work, we consider SPT states at least with charge symmetry (U(1) or Z$_N$) or spin $S^z$ rotation symmetry (U(1) or Z$_N$) in 2D, 3D, and the surface of 3D. If both are U(1), we apply external electromagnetic field / `spin gauge field' to study the charge / spin response. For the SPT examples we consider (i.e. U$_c$(1)$\rtimes$Z$^T_2$, U$_s$(1)$\times$Z$^T_2$, U$_c$(1)$\times$[U$_s$(1)$\rtimes$Z$_2$]; subscripts $c$ and $s$ are short for charge and spin; Z$^T_2$ and Z$_2$ are time-reversal symmetry and $\pi$-rotation about $S^y$, respectively), many variants of Witten effect in the 3D SPT bulk and various versions of anomalous surface quantum Hall effect are defined and systematically investigated. If charge or spin symmetry reduces to Z$_N$ by considering charge-$N$ or spin-$N$ condensate, instead of the linear response approach, we gauge the charge/spin symmetry, leading to a dynamical gauge theory with some remaining global symmetry. The 3D dynamical gauge theory describes a symmetry-enriched topological phase (SET), i.e. a topologically ordered state with global symmetry which admits nontrivial ground state degeneracy depending on spatial manifold topology. For the SPT examples we consider, the corresponding SET states are described by dynamical topological gauge theory with topological BF term and axionic $\Theta$-term in 3D bulk. And the surface of SET is described by the chiral boson theory with quantum anomaly.
56145316
Schrödinger Fermi liquids
A class of strongly interacting many-body fermionic systems in 2+1D non-relativistic conformal field theory is examined via the gauge-gravity duality correspondence. The 5D charged black hole with asymptotic Schrodinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\beta$ at zero temperature. On the larger $\beta$ side, we find the signal of a sharp quasiparticle pole on the spectral function A(k,w), indicating a well-defined Fermi surface. On the smaller $\beta$ side, we find only a hump with no sharp peak for A(k,w), indicating the disappearance of Fermi surface. The dynamical exponent $z$ of quasiparticle dispersion goes from being Fermi-liquid-like $z\simeq1$ scaling at larger $\beta$ to a non-Fermi-liquid scaling $z\simeq 3/2$ at smaller $\beta$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.
14085517
Twisted Gauge Theory Model of Topological Phases in Three Dimensions
We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.
32149826
Bulk viscosity of a gas of massless pions
In the hadronic phase, the dominant configuration of quantum chromodynamics (QCD) with two flavors of massless quarks is a gas of massless pions. We calculate the bulk viscosity ($\ensuremath{\zeta}$) using the Boltzmann equation with the kinetic theory generalized to incorporate the trace anomaly. We find that the dimensionless ratio $\ensuremath{\zeta}/s$, $s$ being the entropy density, is monotonic increasing below $T=120$ MeV, where chiral perturbation theory is applicable. This, combined with previous results, shows that $\ensuremath{\zeta}/s$ reaches its maximum near the phase-transition temperature ${T}_{c}$, while $\ensuremath{\eta}/s$, $\ensuremath{\eta}$ being the shear viscosity, reaches its minimum near ${T}_{c}$ in QCD with massless quarks.
55429933
Symmetry-protected many-body Aharonov-Bohm effect
It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path\char22{}the Aharonov-Bohm effect. Here we examine an Aharonov-Bohm effect on a many-body wave function. Specifically, we study this many-body effect on the gapless edge states of a bulk gapped phase protected by a global symmetry (such as ${\mathbb{Z}}_{N}$)\char22{}the symmetry-protected topological (SPT) states. The many-body analog of spectral shifts, the twisted wave function, and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction.
123418843
The realizations of quantum groups of An−1 and Cn types in q-deformed oscillator systems at classical and quantum levels
In the classical q‐deformed oscillators system, the Poisson bracket realizations of the quantum enveloping algebras of An−1 and Cn types are given in the symplectic space (V,Ω) (without deformation). When the oscillators system is canonically quantized, the Lie bracket realizations of the quantum enveloping algebras of An−1 and Cn types are obtained. The Hopf structures of these quantum enveloping algebras are supplied.
117803245
Unconventional Fermi surface in two-dimensional systems of Dirac fermions
At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as $\mathrm{Im}\Sigma(\omega) \propto |\omega|^{x}$ at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for $0 1$. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.
119180205
The TAOS Project Stellar Variability I. Detection of Low-Amplitude delta Scuti Stars
We analyzed data accumulated during 2005 and 2006 by the Taiwan-American Occultation Survey (TAOS) in order to detect short-period variable stars (periods of <∼ 1 hour) such as δ Scuti. TAOS is designed for the detection of stellar occultation by small-size Kuiper Belt Objects (KBOs) and is operating four 50cm telescopes at an effective cadence of 5Hz. The four telescopes simultaneously monitor the same patch of the sky in order to reduce false positives. To detect short-period variables, we used the Fast Fourier Transform algorithm (FFT) inasmuch as the data points in TAOS light-curves are evenly spaced. Using FFT, we found 41 short-period variables with amplitudes smaller than a few hundredths of a magnitude and periods of about an hour, which suggest that they are low-amplitude δ Scuti stars (LADS). The light-curves of TAOS δ Scuti stars are accessible online at the Time Series Center website (http://timemachine.iic.harvard.edu). Subject headings: (stars: variables:) δ Sct; surveys; methods : data analysis
12584275
Study of charmless hadronic B meson decays to pseudoscalar-vector final states.
We report results of searches for charmless hadronic B meson decays to pseudoscalar( pi(+/-), K+/-, pi(0), or K(0)(S))-vector( rho, K(*), or omega) final states. By using 9.7x10(6) BB pairs collected with the CLEO detector, we report the first observation of B(-)--->pi(-)rho(0), B(0)-->pi(+/-)rho(-/+), and B(-)-->pi(-)omega, which are expected to be dominated by hadronic b-->u transitions. The measured branching fractions are (10.4(+3.3)(-3.4)+/-2.1)x10(-6), (27.6(+8.4)(-7.4)+/-4.2)x10(-6), and (11.3(+3.3)(-2.9)+/-1. 4)x10(-6), respectively. Branching fraction upper limits are set for all of the other decay modes investigated.
118708117
Unconventional behavior of Dirac fermions in three-dimensional gauge theory
We study the unconventional behavior of massless Dirac fermions due to interaction with a U(1) gauge field in two spatial dimensions. At zero chemical potential, the longitudinal and transverse components of gauge interaction are both long-ranged. There is no fermion velocity renormalization since the system respects Lorentz invariance. At finite chemical potential, the Lorentz invariance is explicitly broken by the finite Fermi surface. The longitudinal gauge interaction is statically screened and becomes unimportant, whereas the transverse gauge interaction remains long-ranged and leads to singular renormalization of fermion velocity. The anomalous dimension of fermion velocity is calculated by means of the renormalization group method. We then examine the influence of singular velocity renormalization on several physical quantities, and show that they exhibit different behavior at zero and finite chemical potential.