arXiv subjects

Haruki Watanabe

Publications and source records attributed to Haruki Watanabe.

79 records · Page 5Linked to original sources

arXiv2014

Spontaneous breaking of spacetime symmetries and the inverse Higgs effect

It has been long known that when spacetime symmetry is spontaneously broken, some of the broken generators may not give rise to independent gapless, Nambu-Goldstone excitations. We provide two complementary viewpoints of this phenomenon. On the one hand, we show that the corresponding field degrees of freedom have the same symmetry transformation properties as massive, matter fields. The "inverse Higgs constraints", sometimes employed to eliminate these modes from the theory, are reinterpreted as giving a field parametrization that makes these transformation properties manifest. On the other hand, relations among classical symmetry transformations generally lead to identities for the associated Noether currents that allow saturation of the Ward-Takahashi identities for all the broken symmetries with fewer gapless excitations than suggested by mere counting of broken generators.

hep-ph↗

arXiv2013

Massive Nambu-Goldstone Bosons

Nicolis and Piazza have recently pointed out the existence of Nambu-Goldstone-like excitations in relativistic systems at finite density, whose gap is exactly determined by the chemical potential and the symmetry algebra. We show that the phenomenon is much more general than anticipated and demonstrate the presence of such modes in a number of systems from (anti)ferromagnets in magnetic field to superfluid phases of quantum chromodynamics. Furthermore, we prove a counting rule for these massive Nambu-Goldstone bosons and construct a low-energy effective Lagrangian that captures their dynamics.

hep-th↗

arXiv2013

Redundancies in Nambu-Goldstone Bosons

We propose a simple criterion to identify when Nambu-Goldstone bosons (NGBs) for different symmetries are redundant. It solves an old mystery why crystals have phonons for spontaneously broken translations but no gapless excitations for equally spontaneously broken rotations. Similarly for a superfluid, the NGB for spontaneously broken Galilean symmetry is redundant with phonons. The most nontrivial example is Tkachenko mode for a vortex lattice in a superfluid, where phonons are redundant to the Tkachenko mode which is identified as the Boboliubov mode.

cond-mat.other↗

arXiv2012

Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance

Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. Their number is less than the number of broken generators when some of them form canonically conjugate pairs. The pairing occurs when the generators have a nonzero expectation value of their commutator. For non-semi-simple algebras, central extensions are possible. The underlying geometry of the coset space in general is partially symplectic.

hep-th↗

arXiv2012

Spontaneous breaking of continuous translational invariance

Unbroken continuous translational invariance is often taken as a basic assumption in discussions of spontaneous symmetry breaking (SSB), which singles out SSB of translational invariance itself as an exceptional case. We present a framework which allows us to treat translational invariance on the same footing as other symmetries. It is shown that existing theorems on SSB can be straightforwardly extended to this general case. As a concrete application, we analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on the ground of the general theorems that the Bogoliubov mode stemming from a spontaneously broken internal U(1) symmetry and the longitudinal phonon due to a crystalline order are distinct physical modes.

cond-mat.stat-mech↗

arXiv2011

On the number of Nambu-Goldstone bosons and its relation to charge densities

The low-energy physics of systems with spontaneous symmetry breaking is governed by the associated Nambu-Goldstone (NG) bosons. While NG bosons in Lorentz-invariant systems are well understood, the precise characterization of their number and dispersion relations in a general quantum many-body system is still an open problem. An inequality relating the number of NG bosons and their dispersion relations to the number of broken symmetry generators was found by Nielsen and Chadha. In this paper, we give a presumably first example of a system in which the Nielsen-Chadha inequality is actually not saturated. We suggest that the number of NG bosons is exactly equal to the number of broken generators minus the number of pairs of broken generators whose commutator has a nonzero vacuum expectation value. This naturally leads us to a proposal for a different classification of NG bosons.

hep-ph↗

arXiv2010

Half-integer contributions to the quantum Hall conductivity from single Dirac cones

While the quantum Hall effect in graphene has been regarded as a realization of the anomaly associated with the massless Dirac particle carrying half the usual topological integer, this is hidden due to the doubling of the Dirac cones. In order to confirm the half-integer contribution from each Dirac cone, here we theoretically consider a lattice model in which the relative energy between the two Dirac points is systematically shifted. With an explicit calculation of the topological (Chern) number, we have demonstrated that each Dirac cone does indeed contribute to the Hall conductivity as the half odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) when the Fermi energy traverses the (shifted sets of) Landau levels. The picture is also endorsed, via the bulk-edge correspondence, from the edge mode spectrum for the present model.

cond-mat.mes-hall↗