6 research outputs found
Ground-state fidelity in one-dimensional gapless model
A general relation between quantum phase transitions and the second
derivative of the fidelity (or the "fidelity susceptibility") is proposed. The
validity and the limitation of the fidelity susceptibility in characterizing
quantum phase transitions is thus established. Moreover, based on the
bosonization method, general formulas of the fidelity and the fidelity
susceptibility are obtained for a class of one-dimensional gapless systems
known as the Tomonaga-Luttinger liquid. Applying these formulas to the
one-dimensional spin-1/2 model, we find that quantum phase transitions,
even of the Beresinskii-Kosterlitz-Thouless type, can be signaled by the
fidelity susceptibility.Comment: 4+ pages, no figure, published versio
Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
In this paper, we investigate the fidelity for the Heisenberg chain with the
next-nearest-neighbor interaction (or the model) and analyze its
connections with quantum phase transition. We compute the fidelity between the
ground states and find that the phase transition point of the model
can not be well characterized by the ground state fidelity for finite-size
systems. Instead, we introduce and calculate the fidelity between the first
excited states. Our results show that the quantum transition can be well
characterized by the fidelity of the first excited state even for a small-size
system.Comment: 4 pages, 5 figures, version published in Phys. Rev.
Fidelity approach to quantum phase transitions
We review briefly the quantum fidelity approach to quantum phase transitions
in a pedagogical manner. We try to relate all established but scattered results
on the leading term of the fidelity into a systematic theoretical framework,
which might provide an alternative paradigm for understanding quantum critical
phenomena. The definition of the fidelity and the scaling behavior of its
leading term, as well as their explicit applications to the one-dimensional
transverse-field Ising model and the Lipkin-Meshkov-Glick model, are introduced
at the graduate-student level. In addition, we survey also other types of
fidelity approach, such as the fidelity per site, reduced fidelity,
thermal-state fidelity, operator fidelity, etc; as well as relevant works on
the fidelity approach to quantum phase transitions occurring in various
many-body systems.Comment: 41 pages, 31 figures. We apologize if we omit acknowledging your
relevant works. Do tell. An updated version with clearer figures can be found
at: http://www.phy.cuhk.edu.hk/~sjgu/fidelitynote.pd
Density-functional fidelity approach to quantum phase transitions
We propose a new approach to quantum phase transitions in terms of the
density-functional fidelity, which measures the similarity between density
distributions of two ground states in parameter space. The key feature of the
approach, as we will show, is that the density-functional fidelity can be
measured easily in experiments. Both the validity and versatility of the
approach are checked by the Lipkin-Meshkov-Glick model and the one-dimensional
Hubbard model.Comment: 4 pages, 2 figures, submitted to Chin. Phys. Let
An Almost Perfect Quantum Lattice Action for Low-energy SU(2) Gluodynamics
We study various representations of infrared effective theory of SU(2)
Gluodynamics as a (quantum) perfect lattice action. In particular we derive a
monopole action and a string model of hadrons from SU(2) Gluodynamics. These
are lattice actions which give almost cut-off independent physical quantities
even on coarse lattices. The monopole action is determined by numerical
simulations in the infrared region of SU(2) Gluodynamics. The string model of
hadrons is derived from the monopole action by using BKT transformation. We
illustrate the method and evaluate physical quantities such as the string
tension and the mass of the lowest state of the glueball analytically using the
string model of hadrons. It turns out that the classical results in the string
model is near to the one in quantum SU(2) Gluodynamics.Comment: 39 pages, 10 figure
Quantum Theory of Strings in Abelian Higgs Model
Starting from the Abelian Higgs field theory, we construct the theory of
quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space --
time dimensions in the limit of infinitely thin strings, the conformal anomaly
is absent, and the quantum theory exists. We also study an analogue of the
Aharonov--Bohm effect: the corresponding topological interaction is
proportional to the linking number of the string world sheet and the particle
world trajectory. The creation operators of the strings are explicitly
constructed in the path integral and in the Hamiltonian formulation of the
theory. We show that the Aharonov--Bohm effect gives rise to several nontrivial
commutation relations.Comment: 17 pages, LaTe