185 research outputs found
Scanning the Parameter Space of Holographic Superconductors
We study various physical quantities associated with holographic s-wave
superconductors as functions of the scaling dimensions of the dual condensates.
A bulk scalar field with negative mass squared , satisfying the
Breitenlohner-Freedman stability bound and the unitarity bound, and allowed to
vary in unit intervals, were considered. We observe that all the physical
quantities investigated are sensitive to the scaling dimensions of the dual
condensates. For all the , the characteristic lengths diverge at the
critical temperature in agreement with the Ginzburg-Landau theory. The
Ginzburg-Landau parameter, obtained from these length scales indicates that the
holographic superconductors can be type I or type II depending on the charge
and the scaling dimensions of the dual condensates. For a fixed charge, there
exists a critical scaling dimension, above which a holographic superconductor
is type I, below which it becomes a type II.Comment: 24 pages 47 figure
Holography, Fractionalization and Magnetic Fields
Four dimensional gravity with a U(1) gauge field, coupled to various fields
in asymptotically anti-de Sitter spacetime, provides a rich arena for the
holographic study of the strongly coupled (2+1)-dimensional dynamics of finite
density matter charged under a global U(1). As a first step in furthering the
study of the properties of fractionalized and partially fractionalized degrees
of freedom in the strongly coupled theory, we construct electron star solutions
at zero temperature in the presence of a background magnetic field. We work in
Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source
is cloaked by an event horizon. A key ingredient of our solutions is our
observation that starting with the standard Landau level structure for the
density of states, the electron star limits reduce the charge density and
energy density to that of the free fermion result. Using this result we
construct three types of solution: One has a star in the infra-red with an
electrically neutral horizon, another has a star that begins at an electrically
charged event horizon, and another has the star begin a finite distance from an
electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly
interacting matter in magnetic fields. v2: Updated references and adjusted
some phrasing in the introductio
NR duals in M-theory
We extend the search for supergravity solution duals of non-relativistic
CFTs to supergravity. We consider the internal space to be an
bundle over a product base: and . For
purely M-theoretic , we find only magnetic fluxes preserving
two supersymmetries. is far richer admitting in addition to
magnetic fluxes, various non-trivial electric fluxes which break all
supersymmetry.Comment: 18 pages, Minor corrections and added reference
Families of IIB duals for nonrelativistic CFTs
We show that the recent string theory embedding of a spacetime with
nonrelativistic Schrodinger symmetry can be generalised to a twenty one
dimensional family of solutions with that symmetry. Our solutions include IIB
backgrounds with no three form flux turned on, and arise as near horizon limits
of branewave spacetimes. We show that there is a hypersurface in the space of
these theories where an instability appears in the gravitational description,
indicating a phase transition in the nonrelativistic field theory dual. We also
present simple embeddings of duals for nonrelativistic critical points where
the dynamical critical exponent can take many values z \neq 2.Comment: 1+25 pages. References adde
Application of the group-theoretical method to physical problems
The concept of the theory of continuous groups of transformations has
attracted the attention of applied mathematicians and engineers to solve many
physical problems in the engineering sciences. Three applications are presented
in this paper. The first one is the problem of time-dependent vertical
temperature distribution in a stagnant lake. Two cases have been considered for
the forms of the water parameters, namely water density and thermal
conductivity. The second application is the unsteady free-convective
boundary-layer flow on a non-isothermal vertical flat plate. The third
application is the study of the dispersion of gaseous pollutants in the
presence of a temperature inversion. The results are found in closed form and
the effect of parameters are discussed
A note on the extensivity of the holographic entanglement entropy
We consider situations where the renormalized geometric entropy, as defined
by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the
volume of the entangled region. In general, any holographic geometry that is
`capped' in the infrared region is a candidate for extensivity provided the
growth of minimal surfaces saturates at the capping region, and the induced
metric at the `cap' is non-degenerate. Extensivity is well-known to occur for
highly thermalized states. In this note, we show that the holographic ansatz
predicts the persistence of the extensivity down to vanishing temperature, for
the particular case of conformal field theories in 2+1 dimensions with a
magnetic field and/or electric charge condensates.Comment: 12 pages and 2 figures; one reference added; Significant additions to
section 3, involving new results and a more pedagogical presentatio
Branes at Quantum Criticality
In this paper we propose new non-relativistic p+1 dimensional theory. This
theory is defined in such a way that the potential term obeys the principle of
detailed balance where the generating action corresponds to p-brane action.
This condition ensures that the norm of the vacuum wave functional of p+1
dimensional theory is equal to the partition function of p-brane theory.Comment: 17 pages, references added, typos fixed,v2. minor change
Quantum phase transitions from topology in momentum space
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
physics which emerges in the low-energy corner does not depend on the
complicated details of the system and is relatively simple. It is determined by
the nodes in the fermionic spectrum, which are protected by topology in
momentum space (in some cases, in combination with the vacuum symmetry). Close
to the nodes the behavior of the system becomes universal; and the universality
classes are determined by the toplogical invariants in momentum space. When one
changes the parameters of the system, the transitions are expected to occur
between the vacua with the same symmetry but which belong to different
universality classes. Different types of quantum phase transitions governed by
topology in momentum space are discussed in this Chapter. They involve Fermi
surfaces, Fermi points, Fermi lines, and also the topological transitions
between the fully gapped states. The consideration based on the momentum space
topology of the Green's function is general and is applicable to the vacua of
relativistic quantum fields. This is illustrated by the possible quantum phase
transition governed by topology of nodes in the spectrum of elementary
particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum
Simulations via Analogues: From Phase Transitions to Black Holes", to appear
in Springer lecture notes in physics (LNP
Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
We discuss the general theoretical arguments advanced earlier for the T=0
global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing
between the established and the conjectured. In addition to the well-known
phase of a paramagnetic metal with a "large" Fermi surface (P_L), there is also
an antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide the
details of the derivation of a quantum non-linear sigma-model (QNLsM)
representation of the Kondo lattice Hamiltonian, which leads to an effective
field theory containing both low-energy fermions in the vicinity of a Fermi
surface and low-energy bosons near zero momentum. An asymptotically exact
analysis of this effective field theory is made possible through the
development of a renormalization group procedure for mixed fermion-boson
systems. Considerations on how to connect the AF_S and P_L phases lead to a
global phase diagram, which not only puts into perspective the theory of local
quantum criticality for antiferromagnetic heavy fermion metals, but also
provides the basis to understand the surprising recent experiments in
chemically-doped as well as pressurized YbRh2Si2. We point out that the AF_S
phase still occurs for the case of an equal number of spin-1/2 local moments
and conduction electrons. This observation raises the prospect for a global
phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally,
we discuss the connection between the Kondo breakdown physics discussed here
for the Kondo lattice systems and the non-Fermi liquid behavior recently
studied from a holographic perspective.Comment: (v3) leftover typos corrected. (v2) Published version. 32 pages, 4
figures. Section 7, on the connection between the Kondo lattice systems and
the holographic models of non-Fermi liquid, is expanded. (v1) special issue
of JLTP on quantum criticalit
Quantum Criticality via Magnetic Branes
Holographic methods are used to investigate the low temperature limit,
including quantum critical behavior, of strongly coupled 4-dimensional gauge
theories in the presence of an external magnetic field, and finite charge
density. In addition to the metric, the dual gravity theory contains a Maxwell
field with Chern-Simons coupling. In the absence of charge, the magnetic field
induces an RG flow to an infrared AdS geometry, which is
dual to a 2-dimensional CFT representing strongly interacting fermions in the
lowest Landau level. Two asymptotic Virasoro algebras and one chiral Kac-Moody
algebra arise as {\sl emergent symmetries} in the IR. Including a nonzero
charge density reveals a quantum critical point when the magnetic field reaches
a critical value whose scale is set by the charge density. The critical theory
is probed by the study of long-distance correlation functions of the boundary
stress tensor and current. All quantities of major physical interest in this
system, such as critical exponents and scaling functions, can be computed
analytically. We also study an asymptotically AdS system whose magnetic
field induced quantum critical point is governed by a IR Lifshitz geometry,
holographically dual to a D=2+1 field theory. The behavior of these holographic
theories shares important similarities with that of real world quantum critical
systems obtained by tuning a magnetic field, and may be relevant to materials
such as Strontium Ruthenates.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in
magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A.
Schmitt, H.-U. Ye
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