4,576 research outputs found
Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench
At thermal equilibrium, the concept of effective central charge for massive
deformations of two-dimensional conformal field theories (CFT) is well
understood, and can be defined by comparing the partition function of the
massive model to that of a CFT. This temperature-dependent effective charge
interpolates monotonically between the central charge values corresponding to
the IR and UV fixed points at low and high temperatures, respectively. We
propose a non-equilibrium, time-dependent generalization of the effective
central charge for integrable models after a quantum quench, ,
obtained by comparing the return amplitude to that of a CFT quench. We study
this proposal for a large mass quench of a free boson, where the charge is seen
to interpolate between at , and at
, as is expected. We use our effective charge to define an "Ising
to Tricritical Ising" quench protocol, where the charge evolves from at , to at , the corresponding
values of the first two unitary minimal CFT models. We then argue that the
inverse "Tricritical Ising to Ising" quench is impossible with our methods.
These conclusions can be generalized for quenches between any two adjacent
unitary minimal CFT models. We finally study a large mass quench into the
"staircase model" (sinh-Gordon with a particular complex coupling). At short
times after the quench, the effective central charge increases in a discrete
"staircase" structure, where the values of the charge at the steps can be
computed in terms of the central charges of unitary minimal CFT models. When
the initial state is a pure state, one always finds that , though , generally
oscillates at finite times. We explore how this constraint may be related to RG
flow irreversibility.Comment: Some discussion modified. Title slightly modified. References added.
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Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder
One-dimensional Heisenberg spin 1/2 chains with random ferro- and
antiferromagnetic bonds are realized in systems such as . We have investigated numerically the thermodynamic properties of a
generic random bond model and of a realistic model of by the quantum Monte Carlo loop algorithm. For the first time we
demonstrate the separation into three different temperature regimes for the
original Hamiltonian based on an exact treatment, especially we show that the
intermediate temperature regime is well-defined and observable in both the
specific heat and the magnetic susceptibility. The crossover between the
regimes is indicated by peaks in the specific heat. The uniform magnetic
susceptibility shows Curie-like behavior in the high-, intermediate- and
low-temperature regime, with different values of the Curie constant in each
regime. We show that these regimes are overlapping in the realistic model and
give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for
publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999
A Note on ADE-Spectra in Conformal Field Theory
We demonstrate that certain Virasoro characters (and their linear
combinations) in minimal and non-minimal conformal models which admit
factorized forms are manifestly related to the ADE series. This permits to
extract quasi-particle spectra of a Lie algebraic nature which resembles the
features of Toda field theory. These spectra possibly admit a construction in
terms of the -generators. In the course of our analysis we establish
interrelations between the factorized characters related to the parafermionic
models, the compactified boson and the minimal models.Comment: 7 pages Late
Entanglement entropy of aperiodic quantum spin chains
We study the entanglement entropy of blocks of contiguous spins in
non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg,
XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and
relevant aperiodic modulations, the entanglement entropy is found to be a
logarithmic function of the block size with log-periodic oscillations. The
effective central charge, c_eff, defined through the constant in front of the
logarithm may depend on the ratio of couplings and can even exceed the
corresponding value in the homogeneous system. In the strong modulation limit,
the ground state is constructed by a renormalization group method and the
limiting value of c_eff is exactly calculated. Keeping the ratio of the block
size and the system size constant, the entanglement entropy exhibits a scaling
property, however, the corresponding scaling function may be nonanalytic.Comment: 6 pages, 2 figure
Noise optimized eigenfilter design of time-domain equalizers for DMT systems
The design of time-domain equalizers or TEQs for discrete multitone modulation (DMT) systems has recently received much attention. In this paper, we present a generalization of one such design method which takes into account the noise observed in a DMT channel. Furthermore, we show how this generalization can be used for the design of fractionally spaced equalizers or FSEs. Experimental results are presented showing that our design method performs better than other known techniques
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