arXiv subjects

K. Shizuya

Publications and source records attributed to K. Shizuya.

33 records · Page 2Linked to original sources

arXiv2006

Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

The effect of quantum fluctuations on Bogomol'nyi-Prasad-Sommerfield (BPS)-saturated topological excitations in supersymmetric theories is studied. Focus is placed on a sequence of topological excitations that derive from the same classical soliton or vortex in lower dimensions and it is shown that their quantum characteristics, such as the spectrum and profile, differ critically with the dimension of spacetime. In all the examples examined the supercharge algebra retains its classical form although short-wavelength fluctuations may modify the operator structure of the central charge, yielding an anomaly. The central charge, on taking the expectation value, is further affected by long-wavelength fluctuations, and this makes the BPS-excitation spectra only approximately calculable in some low-dimensional theories. In four dimensions, in contrast, holomorphy plays a special role in stabilizing the BPS-excitation spectra against quantum corrections. The basic tool in our study is the superfield supercurrent, from which the supercharge algebra with a central extension is extracted in a supersymmetric setting. A general method is developed to determine the associated superconformal anomaly by considering dilatation directly in superspace.

hep-th↗

arXiv2005

Central charge and renormalization in supersymmetric theories with vortices

Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one loop while the spectrum of the elementary excitations receives higher-order corrections.

hep-th↗

arXiv2004

Topological-charge anomalies in supersymmetric theories with domain walls

Domain walls in 1+2 dimensions are studied to clarify some general features of topological-charge anomalies in supersymmetric theories, by extensive use of a superfield supercurrent. For domain walls quantum modifications of the supercharge algebra arise not only from the short-distance anomaly but also from another source of long-distance origin, induced spin in the domain-wall background, and the latter dominates in the sum. A close look into the supersymmetric trace identity, which naturally accommodates the central-charge anomaly and its superpartners, shows an interesting consequence of the improvement of the supercurrent: Via an improvement the anomaly in the central charge can be transferred from induced spin in the fermion sector to an induced potential in the boson sector. This fact reveals a dual character, both fermionic and bosonic, of the central-charge anomaly, which reflects the underlying supersymmetry. The one-loop superfield effective action is also constructed to verify the anomaly and BPS saturation of the domain-wall spectrum.

hep-th↗

arXiv2004

Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with N=1 supersymmetry. Extensive use is made of the superfield supercurrent, that places the supercurrent J^{mu}_{alpha}, energy-momentum tensor Theta^{mu nu} and topological current zeta^{mu} in a supermultiplet, to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of (J^{mu}_{alpha}, Theta^{mu nu}, zeta^{mu}) is kept exact while the topological current zeta^μ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.

hep-th↗

arXiv2004

Single-mode approximation and effective Chern-Simons theories for quantum Hall systems

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern-Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern-Simons theory. For single-layer systems the effective theory agrees with the standard Chern-Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.

cond-mat.mes-hall↗

arXiv2003

Electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling

The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode approximation, with emphasis on clarifying the nature of the low-lying neutral collective mode responsible for interlayer tunneling phenomena. A long-wavelength effective theory, consisting of the collective mode as well as the cyclotron modes, is constructed. It is seen explicitly from the electromagnetic response that gauge invariance is kept exact, this implying, in particular, the absence of the Meissner effect in bilayer systems. Special emphasis is placed on exploring the advantage of looking into quantum Hall systems through their response; in particular, subtleties inherent to the standard Chern-Simons theories are critically examined.

cond-mat.mes-hall↗

arXiv2002

Electromagnetic response and effective gauge theory of double-layer quantum Hall systems

We report on an effective gauge theory of double-layer quantum Hall systems, that is constructed via bosonization from the response of incompressible states without referring to composite bosons and fermions. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems, and the single-mode approximation is used to study them. The effective theory consists of three vector fields representing one interlayer collective mode and two cyclotron modes, and properly incorporates the spectrum of collective excitations on the right scale of the Coulomb interaction. Special emphasis is placed on exploring the advantage of looking into quantum Hall systems through their response; in particular, subtleties inherent to the standard Chern-Simons theories are critically examined.

cond-mat.mes-hall↗

arXiv2002

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.

cond-mat.mes-hall↗

arXiv2001

Effective vector-field theory and long-wavelength universality of the fractional quantum Hall effect

We report on an effective vector-field theory of the fractional quantum Hall effect that takes into account projection to Landau levels. The effective theory refers to neither the composite-boson nor composite-fermion picture, but properly reproduces the results consistent with them, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states. In particular, the dual-field Lagrangian of Lee and Zhang is obtained, and an argument is given to verify the identification by Goldhaber and Jain of a composite fermion as a dressed electron. The generalization to double-layer systems is also remarked on.

cond-mat.mes-hall↗

arXiv2001

Bosonization and effective vector-field theory of the fractional quantum Hall effect

The electromagnetic characteristics of the fractional quantum Hall states are studied by formulating an effective vector-field theory that takes into account projection to the exact Landau levels from the beginning. The effective theory is constructed, via bosonization, from the electromagnetic response of an incompressible and uniform state. It does not refer to either the composite-boson or composite-fermion picture, but properly reproduces the results of the standard bosonic and fermionic Chern-Simons approaches, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states and the associated quasiparticles. In particular, the dual-field Lagrangian of Lee and Zhang is obtained without invoking the composite-boson picture. An argument is also given to verify, within a vector-field version of the fermionic Chern-Simons theory, the identification by Goldhaber and Jain of a composite fermion as a dressed electron.

cond-mat.mes-hall↗

arXiv2000

Current distribution in Hall bars and breakdown of the quantum Hall effect

A numerical study is made of current distribution in small Hall bars with disorder. It is observed, in particular, that in the Hall-plateau regime the Hall current tends to concentrate near the sample edges while it diminishes on average in the sample interior as a consequence of localization. Also reported is another numerical experiment on a related, but rather independent topic, the breakdown of the quantum Hall effect. It is pointed out that the competition of the Hall field with disorder in the sample interior, an intra-subband process, can account for both the magnitude and magnetic-field dependence (proportional to B^{3/2}) of the critical breakdown fields observed experimentally.

cond-mat.mes-hall↗

arXiv1999

Field-induced breakdown of the quantum Hall effect

A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states decreases exponentially with the Hall field, with its dependence on the magnetic and electric field summarized in a simple scaling law. The physical picture underlying the scaling law is clarified. This intra-subband process, the competition of the Hall field with disorder, leads to critical breakdown fields of magnitude of a few hundred V/cm, consistent with observations, and accounts for their magnetic-field dependence \propto B^{3/2} observed experimentally. Some testable consequences of the scaling law are discussed.

cond-mat.mes-hall↗

arXiv1998

Numerical study of current distributions in finite planar Hall samples with disorder

A numerical study is made of current distributions in finite-width Hall bars with disorder and some theoretical observations are verified. The equilibrium current and the Hall current are substantially different in distribution. It is observed that in the Hall-plateau regime the Hall current tends to concentrate near the sample edges while it diminishes on average in the sample interior as a consequence of localization. The edge states themselves scarcely affect both the equilibrium and Hall currents in the plateau regime. The sample edge combines with disorder to efficiently delocalize electrons near the edge while the Hall field competes with disorder to delocalize electrons in the sample interior. A possible mechanism is suggested for the breakdown of the quantum Hall effect.

cond-mat.mes-hall↗

arXiv1997

Current distributions and the de Haas-van Alphen oscillation in a planar system of Hall electrons

The current distribution is studied for a finite-width two-dimensional system of Hall electrons, with a clear distinction drawn between the equilibrium edge current and the Hall current. It is pointed out that both the distribution and direction of the equilibrium edge current change dramatically as the number of electron edge states increases, and that this alternating edge current is another manifestation of the de Haas-van Alphen effect. The Hall-current distribution is substantially different from the edge current distribution, and it is shown numerically that the fast-traveling electrons along the sample edge are not the main carriers of the Hall current.

cond-mat↗

arXiv1997

Localization and exact current compensation in the quantum Hall effect

A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of localization. It is shown, in particular, that the immobility of localized electron states and current compensation by extended electron states, both crucial for quantization of the Hall conductance, are derived through the operation of magnetic translation of localized electron states alone. They actually are consequences of gauge invariance and hold under general circumstances with both level mixing and electron edge states taken into account.

cond-mat.mes-hall↗