Publications (157)448.99 Total impact
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ABSTRACT: In a recent study of the selfadjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the selfadjoint extension parameter, the bound states lo calized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the RungeLenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r potential.  [Show abstract] [Hide abstract]
ABSTRACT: In analogy to the pions in chiral perturbation theory, the transverse fluctuations of a confining string in Yang–Mills theory are described by a systematic lowenergy effective field theory. The predictions of the effective theory at the twoloop level are in quantitative agreement with highprecision Monte Carlo data obtained from lattice gauge theory. The decay and ultimate breaking of strings connecting charges in higherdimensional representations of the gauge group are also investigated. 
Article: Walking near a conformal fixed point
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ABSTRACT: Based on a symmetry analysis of the microscopic Hubbard and tJ models, a systematic lowenergy effective field theory is constructed for holedoped antiferromagnets on the honeycomb lattice. In the antiferromagnetic phase, doped holes are massive due to the spontaneous breakdown of the $SU(2)_s$ symmetry, just as nucleons in QCD pick up their mass from spontaneous chiral symmetry breaking. In the broken phase the effective action contains a singlederivative term, similar to the ShraimanSiggia term in the square lattice case. Interestingly, an accidental continuous spatial rotation symmetry arises at leading order. As an application of the effective field theory we consider onemagnon exchange between two holes and the formation of twohole bound states. As an unambiguous prediction of the effective theory, the wave function for the ground state of two holes bound by magnon exchange exhibits $f$wave symmetry.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a 1parameter family of selfadjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seems to violate the Heisenberg uncertainty relation. We use this as a motivation to derive a generalized uncertainty relation valid for an arbitrarily shaped quantum dot with general perfectly reflecting walls in $d$ dimensions. In addition, a general uncertainty relation for nonHermitean operators is derived and applied to the nonHermitean momentum operator in a quantum dot. We also consider minimal uncertainty wave packets in this situation, and we prove that the spectrum depends monotonically on the selfadjoint extension parameter. In addition, we construct the most general boundary conditions for semiconductor heterostructures such as quantum dots, quantum wires, and quantum wells, which are characterized by a 4parameter family of selfadjoint extensions. Finally, we consider perfectly reflecting boundary conditions for relativistic fermions confined to a finite volume or localized on a domain wall, which are characterized by a 1parameter family of selfadjoint extensions in the $(1+1)$d and $(2+1)$d cases, and by a 4parameter family in the $(3+1)$d and $(4+1)$d cases.  [Show abstract] [Hide abstract]
ABSTRACT: The twodimensional (2D) spin1/2 Heisenberg antiferromagnet with exchange coupling J is investigated on a periodic square lattice of spacing a at very small temperatures using the loopcluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic lowenergy effective field theory for the staggered magnetization order parameter. The lowenergy parameters of the effective theory, i.e., the staggered magnetization density Ms=0.307 43(1)/a2, the spin stiffness ρs=0.180 81(11)J, and the spin wave velocity c=1.6586(3)Ja, are determined with very high precision. Our study may serve as a test case for the comparison of lattice quantum chromodynamics Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.  [Show abstract] [Hide abstract]
ABSTRACT: Using an improved estimator in the loopcluster algorithm, we investigate the constraint effective potential of the magnetization in the spin $\tfrac{1}{2}$ quantum XY model. The numerical results are in excellent agreement with the predictions of the corresponding lowenergy effective field theory. After its lowenergy parameters have been determined with better than permille precision, the effective theory makes accurate predictions for the constraint effective potential which are in excellent agreement with the Monte Carlo data. This shows that the effective theory indeed describes the physics in the lowenergy regime quantitatively correctly.  [Show abstract] [Hide abstract]
ABSTRACT: The logarithmic broadening predicted by the systematic lowenergy effective field theory for the confining string has recently been verified in numerical simulations of (2+1)d SU(2) lattice YangMills theory at zero temperature. The same effective theory predicts linear broadening of the string at low nonzero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the lowenergy constants of the effective theory have already been fixed at zero temperature. It yields very good agreement between the underlying YangMills theory and the effective string theory. 
Article: Topological Lattice Actions
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ABSTRACT: We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1d O(2) and O(3) model, as well as Monte Carlo simulations of the 2d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2d O(3) model the topological susceptibility \chi_t = \l< Q^2 >/V is logarithmically divergent in the continuum limit. Still, at nonzero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit. Comment: 37 pages, 11 figures  [Show abstract] [Hide abstract]
ABSTRACT: The color flux tube connecting a static quarkantiquark pair in YangMills theory supports massless transverse fluctuations, which are the Goldstone bosons of spontaneously broken translation invariance. Just as in chiral perturbation theory, the dynamics of these Goldstone bosons is described by a systematic lowenergy effective field theory. We use the effective theory to calculate the width of the fluctuating string at the 2loop level, using both cylindrical and toroidal boundary conditions. At zero temperature, the string width diverges logarithmically with the quarkantiquark distance r. On the other hand, at low but nonzero temperature T = 1/\beta, for r >> \beta, the string width diverges linearly.  [Show abstract] [Hide abstract]
ABSTRACT: The 2d spin 1/2 Heisenberg antiferromagnet with exchange coupling $J$ is investigated on a periodic square lattice of spacing $a$ at very small temperatures using the loopcluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic lowenergy effective field theory for the staggered magnetization order parameter. The lowenergy parameters of the effective theory, i.e.\ the staggered magnetization density ${\cal M}_s = 0.30743(1)/a^2$, the spin stiffness $\rho_s = 0.18081(11) J$, and the spin wave velocity $c = 1.6586(3) J a$ are determined with very high precision. Our study may serve as a test case for the comparison of lattice QCD Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the stability of strings connecting charges Q in the representation {2Q+1} of SU(2) YangMills theory in (2+1) dimensions. While the fundamental {2}string between two charges Q=1/2 is unbreakable and stable, the string connecting static charges transforming under any other representation Q>1/2 is unstable and decays. A charge Q=1 can be completely screened by gluons and so the adjoint {3}string ultimately breaks. A charge Q=3/2 can be only partially screened to a fundamental charge Q=1/2. Thus, stretching a {4}string beyond a critical length, it decays into the stable {2}string by gluon pair creation. The complete breaking of a {5}string happens in two steps, it first decays into a {3}string and then breaks completely. A phenomenological constituent gluon model provides a good quantitative description of the energy of the screened charges at the ends of an unstable string. Comment: 7 pages, 2 figures, contribution to The XXVII International Symposium on Lattice Field Theory, July 2631, 2009, Peking University, Beijing, China  [Show abstract] [Hide abstract]
ABSTRACT: We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic lowenergy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case both the microscopic and the effective theory can be solved analytically. In this way the lowenergy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The lowenergy behavior at halffilling as well as in the single and twohole sectors is described exactly by the systematic lowenergy effective field theory. In particular, for weakly bound twohole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic lowenergy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.  [Show abstract] [Hide abstract]
ABSTRACT: We consider wave packets of free particles with a general energymomentum dispersion relation $E(p)$. The spreading of the wave packet is determined by the velocity $v = \p_p E$. The positionvelocity uncertainty relation $\Delta x \Delta v \geq {1/2} < \p_p^2 E >$ is saturated by minimal uncertainty wave packets $\Phi(p) = A \exp( \alpha E(p) + \beta p)$. In addition to the standard minimal Gaussian wave packets corresponding to the nonrelativistic dispersion relation $E(p) = p^2/2m$, analytic calculations are presented for the spreading of wave packets with minimal positionvelocity uncertainty product for the lattice dispersion relation $E(p) =  \cos(p a)/m a^2$ as well as for the relativistic dispersion relation $E(p) = \sqrt{p^2 + m^2}$. The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that baryon chiral perturbation theory, i.e., the low‐energy effective theory for pions and nucleons in quantum chromodynamics, has its condensed matter analog: A low‐energy effective theory describing magnons as well as holes (or electrons) doped into antiferromagnets. We briefly present a symmetry analysis of the Hubbard and t‐J‐type models, and review the construction of the leading terms in the effective Lagrangian. As a nontrivial application we study different phases of hole‐ and electron‐doped antiferromagnets—in particular, we investigate whether a so‐called spiral phase with an inhomogeneous staggered magnetization (order parameter) may be stable. We would like to emphasize that the effective theory is universal and makes model‐independent predictions for a large class of systems, whereas the material‐specific properties enter the effective theory only through the numerical values of a few low‐energy parameters.  [Show abstract] [Hide abstract]
ABSTRACT: We employ an improved estimator to calculate the constraint effective potential of the staggered magnetization in the spin quantum Heisenberg model using a loopcluster algorithm. The first and second moment of the probability distribution of the staggered magnetization are in excellent agreement with the predictions from the systematic lowenergy magnon effective field theory. We also compare the Monte Carlo data with the universal shape of the constraint effective potential of the staggered magnetization and study its approach to the convex effective potential in the infinite volume limit. In this way the higherorder lowenergy parameter k0 is determined from a fit to the numerical data.  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by possible applications to the antiferromagnetic precursor of the hightemperature superconductor Na$_x$CoO$_2\cdot$yH$_2$O, we use a systematic lowenergy effective field theory for magnons and holes to study different phases of doped antiferromagnets on the honeycomb lattice. The effective action contains a leading singlederivative term, similar to the ShraimanSiggia term in the square lattice case, which gives rise to spirals in the staggered magnetization. Depending on the values of the lowenergy parameters, either a homogeneous phase with four or a spiral phase with two filled hole pockets is energetically favored. Unlike in the square lattice case, at leading order the effective action has an accidental continuous spatial rotation symmetry. Consequently, the spiral may point in any direction and is not necessarily aligned with a lattice direction. 
Article: Loopcluster simulation of the zeroand onehole sectors of the tJ model on the honeycomb lattice
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ABSTRACT: Inspired by the unhydrated variant of the superconducting material NaxCoO2⋅yH2O at x=1/3, we study the tJ model on a honeycomb lattice by using an efficient loopcluster algorithm. The lowenergy physics of the undoped system and of the singlehole sector is described by a systematic lowenergy effective field theory. The staggered magnetization per spin M̃s=0.2688(3), the spin stiffness ρs=0.102(2)J, the spinwave velocity c=1.297(16)Ja, and the kinetic mass M′ of a hole are obtained by fitting the numerical Monte Carlo data to the effective field theory predictions.  [Show abstract] [Hide abstract]
ABSTRACT: A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is wellknown that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the $1/r$ and $r^2$ potentials, one thus expects some hidden accidental symmetry, in this case with infinitedimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a RungeLenz vector. After identifying the corresponding accidental symmetry algebra, we reanalyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the $\theta$vacuum angle in nonAbelian gauge theories, quantum effects due to two selfadjoint extension parameters $\theta_x$ and $\theta_y$ explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics. 
Article: From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
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ABSTRACT: Using a loopcluster algorithm we investigate the spin 1/2 Heisenberg antiferromagnet on a square lattice with exchange coupling $J$ and an additional fourspin interaction of strength $Q$. We confirm the existence of a phase transition separating antiferromagnetism at $J/Q > J_c/Q$ from a valence bond solid (VBS) state at $J/Q < J_c/Q$. Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as $80^2$, we find evidence for a weak first order phase transition. We also present a detailed study of the antiferromagnetic phase. For $J/Q > J_c/Q$ the staggered magnetization, the spin stiffness, and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic lowenergy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at $J/Q < J_c/Q$, and we show that long but finite antiferromagnetic correlations are still present. Comment: 21 pages, 10 figures
Publication Stats
4k  Citations  
448.99  Total Impact Points  
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Institutions

2014

Albert Einstein Medical Center
Filadelfia, Pennsylvania, United States


19922014

Universität Bern
 Institute for Theoretical Physics
Berna, Bern, Switzerland


19942013

Massachusetts Institute of Technology
 • Laboratory for Nuclear Science
 • Center for Theoretical Physics
 • Department of Physics
Cambridge, Massachusetts, United States 
Forschungszentrum Jülich
Jülich, North RhineWestphalia, Germany


19871989

Universität Hamburg
 II. Institut für Theoretische Physik
Hamburg, Hamburg, Germany
