We study SU(2) Yang-Mills quantum mechanics with N=2,4,8 and 16 supercharges. This describes the non-relativistic dynamics of a pair of D0-branes moving in d=3,4,6 and 10 spacetime dimensions respectively. We show that as the D0-branes orbit, states undergo a Berry holonomy described by the four Hopf maps. For the N=2 theory, the associated Hopf map is the Mobius bundle and its effect is to turn the D0-branes into anyons with exchange statistics +i and -i. For the N=4,8 and 16 theories, the Hopf maps give rise to Berry connections that are familiar to physicists: the U(1) Dirac monopole; the SU(2) Yang monopole; and the SO(8) octonionic monopole.
We construct a holographic model for Josephson junctions with a defect system of a Dp brane intersecting a D(p+2) brane. In addition to providing a geometrical picture for the holographic dual, this leads us very naturally to suggest the possibility of non-Abelian Josephson junctions characterized in terms of the topological properties of the branes. The difference between the locations of the endpoints of the Dp brane on either side of the defect translates into the phase difference of the condensate in the Josephson junction. We also add a magnetic flux on the D(p+2) brane and allow it evolv…
We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R^5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.
Berry's connection is computed in the USp(2k) matrix model. In T dualized quantum mechanics, the Berry phase exhibits a residual interaction taking place at a distance m_(f) from the orientifold surface via the integration of the fermions in the fundamental representation. This is interpreted as a coupling of the magnetic D2 with the electric D4 branes. We make a comment on the Berry phase associated with the 6D nonabelian gauge anomaly whose cancellation selects the number of flavours n_f=16.
We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These vector fields exhibit kinks at the interval boundary, thus together with their central extension they differ from usual elements of the Virasoro algebra. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which diff…
In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations. Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R^{4n} satisfies a generalization of the self-dual Yang-Mills equations. Upon dimensional reduction, these become the tt* equations. We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on the parameter of space/space noncommtativity.
For the generalized chiral Schwinger model defined on the circle, a direct calculation of the zero curvature part of the vacuum Berry phase connection is given. Although this part does not contribute to the curvature, it is shown to attach several features to the total connection and to produce a physical background of linearly rising electric fields.
We show the presence of a topological (Berry) phase in the time evolution of a mixed state. For the case of mixed neutrinos, the Berry phase is a function of the mixing angle only.
In this paper we define a non-dynamical phase for a spin-1/2 particle in a rotating magnetic field in the non-adiabatic non-cyclic case, and this phase can be considered as a generalized Berry phase. We show that this phase reduces to the geometric Berry phase, in the adiabatic limit, up to a factor independent of the parameters of the system. We could add an arbitrary phase to the eigenstates of the Hamiltonian due to the gauge freedom. Then, we fix this arbitrary phase by comparing our Berry phase in the adiabatic limit with the Berry's result for the same system. Also, in the extreme non-ad…
We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons one-form), whereas we propose that a similar integral but over five dimensional parameter space (an integral of the Chern-Simons five-form) is suitable to define a non-Abelian Berry phase. We study its global topological aspects and show that it is indeed quantized into two values. We also discuss its close relationship with the nonperturbative anomalies.
We construct the kinetic theory in ($1+2d$)-dimensional phase space and time when all abelian and nonabelian phase-space Berry curvatures are nonzero. Then we calculate anomalous transports induced by the Berry curvatures on the basis of the kinetic theory. As an example, we study anomalous charge and spin transports induced by the SU($2$) Berry curvatures. We also derive the topological effective theory to reproduce the transports in insulators calculated from the kinetic theory. Such an effective theory is given by the nonabelian phase space Chern-Simons theory.
Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks.
The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious since the chemical potential may not appear after the Legendre transformation. The geometric phase (Pancharatnam-Berry phase) results from the geometrical properties of the parameter space of the Hamiltonian, which is calculated from the Berry connection. In this paper, using the formalism of the Berry phase, we show that the chemical potential defined by the …
We formulate the dynamics of local order parameters by extending the recently developed adiabatic spinwave theory involving the Berry curvature, and derive a formula showing explicitly the role of the Berry phase in determining the spectral form of the low-lying collective modes. For antiferromagnetic spin chains, the Berry phase becomes a topological invariant known as the Chern number. Our theory predicts the existence of the Haldane gap for a topologically trivial ground state, and a linear dispersion of low-lying excitations for a non-trivial ground state.
We consider the Doubly Special Relativity (DSR) generalization of Dirac equation in an external potential in the Magueijo-Smolin base. The particles obey a modified energy-momentum dispersion relation. The semiclassical diagonalization of the Dirac Hamiltonian reveals the intrinsic Berry phase effects in the particle dynamics.
It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article pre…
In 1984 Michael Berry discovered that an isolated eigenstate of an adiabatically changing periodic Hamiltonian $H(t)$ acquires a phase, called the Berry phase. We show that under very general assumptions the adiabatic approximation of the phase of the zeta-regularized determinant of the imaginary-time Schrodinger operator with periodic Hamiltonian is equal to the Berry phase.
The effect of Generalized Uncertainty Principle (GUP) on Berry phase is studied using the perturbation approach and up to the first order of approximation. Thereinafter, the obtained results are extended to a quantum ring in which two types of spin-orbit interactions, including Rashba and Dresselhaus interactions, can be felt by electrons. Comparing the final results with the accuracy of Berry phase detectors, one can find an upper bound on GUP parameter as $β_{0}<10^{46}$ and $β_{0}<10^{51}$ from Rashba and Dresselhaus interactions, respectively, in agreement with previous results.
We propose the lattice QCD calculation of the Berry phase which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.
We modify the time-dependent electric potential of the Paul trap from a sinusoidal waveform to a square waveform. The exact quantum motion and the Berry's phase of an electron in the modified Paul trap are found in an analytically closed form. We consider a scheme to detect the Berry's phase by a Bohm-Aharonov-type interference experiment and point out a critical property which renders it practicable.
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting fermionic systems. We start with reviewing the semi-classical kinetic theory with Berry phase for a non-interacting ensemble of fermions -- a Berry Fermi gas -- which might be far-from-equilibrium. We particularly review the famous Berry phase contribution to the anomalous Hall current. We then provide a concrete and general path integral derivation for the…
The monopole-like singularity of Berry's adiabatic phase in momentum space and associated anomalous Poisson brackets have been recently discussed in various fields. With the help of the results of an exactly solvable version of Berry's model, we show that Berry's phase does not lead to the deformation of the principle of quantum mechanics in the sense of anomalous canonical commutators. If one should assume Berry's phase of genuine Dirac monopole-type, which is assumed to hold not only in the adiabatic limit but also in the non-adiabatic limit, the deformation of the principle of quantum mecha…
When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing---a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds…
For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in gravitational spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFT. This variable corresponds to a loop integral in the bulk. Through this loop integral, non-factorization becomes apparent in the dual entangled CFTs. Further…
We derive an analogue of the Berry phase associated with inflationary cosmological perturbations of quantum mechanical origin by obtaining the corresponding wavefunction. We have further shown that cosmological Berry phase can be completely envisioned through the observable parameters, viz. spectral indices. Finally, physical significance of this phase is discussed from the point of view of theoretical and observational aspects with some possible consequences of this quantity in inflationary cosmology.
We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases …
Berry phase in axion physics, SM global structure, and generalized symmetries
School of Physics, Peking University（北京大学物理学院）；School of Physics, Zhengzhou University（郑州大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）；Key Laboratory of Beam Technology of Ministry of Education, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院教育部光束技术重点实验室）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）
We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed exactly thanks to the Maurer-Cartan form on the Virasoro group, and they persist after combining left- and right-moving sectors. Thinking of Virasoro representations as particles in AdS_3 dressed with boundary gravitons, the Berry phases associated with Brown-Henneaux diffeomorphisms provide a gravitational extension of Thomas precession.
We study the Berry phase in neutrino oscillations for both Dirac and Majorana neutrinos. In order to have a Berry phase, the neutrino oscillations must occur in a varying medium, the neutrino-background interactions must depend on at least two independent densities, and also there must be CP violation if the neutrino interactions with matter are mediated only by the standard model W and Z boson exchanges which implies that there must be at least three generations of neutrinos. The CP violating Majorana phases do not play a role in generating a Berry phase. We show that a natural way to satisfy…
