1,722,540 research outputs found
Yang-Lee zeros of the Yang-Lee model
Full text linkTo understand the distribution of the Yang-Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the 2D Yang-Lee model. The grand-canonical partition function of this quantum field theory, as a function of the fugacity z and the inverse temperature β, can be computed in terms of the thermodynamics Bethe Ansatz based on its exact S-matrix. We extract the Yang-Lee zeros in the complex plane by using a sequence of polynomials of increasing order N in z which converges to the grand-canonical partition function. We show that these zeros are distributed along curves which are approximate circles as it is also the case of the zeros for purely free theories. There is though an important difference between the interactive theory and the free theories, for the radius of the zeros in the interactive theory goes continuously to zero in the high-temperature limit while in the free theories it remains close to 1 even for small values of β, jumping to 0 only at
Functional renormalization group approach to the Yang-Lee edge singularity
Full text linkWe determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ⋲ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG ß functions is discussed and we estimate the error associated with O(Ә⁴) truncations of the scale-dependent e ective action
Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
Full text linkWe extend the Yang-Lee theory to quantum phase transitions to show how
singularity enters the phase transition points in one-dimensional many-body
systems. We primarily focus on the distribution of Yang-Lee zeros and its
associated Yang-Lee edge singularity of two prototypical models: the
Su-Schrieffer-Heeger (SSH) model and the XXZ spin chain. By taking the
zero-temperature limit, we show how the Yang-Lee zeros approach the quantum
phase transition points on the complex plane of parameters. To characterize the
edge singularity induced by Yang-Lee zeros in quantum phase transition, we
introduce the entanglement entropy of the ground state to show the edges of
Yang-Lee zeros lead to the entanglement transition. We further show our results
are also applicable to the general non-interacting parity-time-symmetric
Hamiltonians.Comment: 5 pages, 2 figures+9 page
Engineering Yang-Lee anyons via Majorana bound states
Full text linkWe propose the platform of a Yang-Lee anyon system which is constructed from
Majorana bound states in topological superconductors. Yang-Lee anyons,
described by the non-unitary conformal field theory with the central charge
, are non-unitary counterparts of Fibonacci anyons, obeying the same
fusion rule, but exhibiting non-unitary non-Abelian braiding statistics. We
consider a topological superconductor junction system coupled with dissipative
electron baths, which realizes a non-Hermitian interacting Majorana system.
Numerically estimating the central charge, we examine the condition that the
non-Hermitian Majorana system can simulate the Ising spin model of the Yang-Lee
edge singularity, and confirm that, by controlling model parameters in a
feasible way, the Yang-Lee edge criticality is realized. On the basis of this
scenario, we present the scheme for the fusion, measurement and braiding of
Yang-Lee anyons in our proposed setup.Comment: 12 pages, 11 figure
Gravitational Yang-Lee Model. Four Point Function
No full textThe four-point perturbative contribution to the spherical partition function of the gravitational Yang-Lee model is evaluated numerically. An effective integration procedure is due to a convenient elliptic parameterization of the moduli space. At certain values of the ``spectator'' parameter the Liouville four-point function involves a number of ``discrete terms'' which have to be taken into account separately. The classical limit, where only discrete terms contribute, is also discussed. In addition, we conjecture an explicit expression for this partition function at the ``second solvable point'' where the spectator matter is in fact another (Yang-Lee) minimal model
Yang-Lee zeros for real-space condensation
No full textUsing the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by a pressure change. The exact solution allows one to read off the scaling of the density of zeros at the critical point and the angle at which the locus of zeros hits the critical point. Since the order of the phase transition and critical exponents can be tuned with a single parameter for several families of weights, the model provides a useful testing ground for verifying various relations between the distribution of zeros and the critical behavior, as well as for exploring the behavior of physical quantities in the mesoscopic regime, i.e., systems of large but finite size. The main result is that asymptotically the Yang-Lee zeros are images of a conformal mapping, given by the generating function for the weights, of uniformly distributed complex phases
Yang-Lee zeros for real-space condensation
No full textUsing the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by a pressure change. The exact solution allows one to read off the scaling of the density of zeros at the critical point and the angle at which the locus of zeros hits the critical point. Since the order of the phase transition and critical exponents can be tuned with a single parameter for several families of weights, the model provides a useful testing ground for verifying various relations between the distribution of zeros and the critical behavior, as well as for exploring the behavior of physical quantities in the mesoscopic regime, i.e., systems of large but finite size. The main result is that asymptotically the Yang-Lee zeros are images of a conformal mapping, given by the generating function for the weights, of uniformly distributed complex phases
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Embedding the Yang-Lee Quantum Criticality in Open Quantum Systems
Full text linkThe Yang-Lee edge singularity is a quintessential nonunitary critical
phenomenon accompanied by anomalous scaling laws. However, an imaginary
magnetic field involved in this critical phenomenon makes its physical
implementation difficult. By invoking the quantum-classical correspondence to
embed the Yang-Lee edge singularity in a quantum system with an ancilla qubit,
we demonstrate a physical realization of the nonunitary quantum criticality in
an open quantum system. Here the nonunitary criticality is identified with the
singularity at an exceptional point caused by postselection of quantum
measurement.Comment: 6 + 9 pages, 1 + 0 figure, 0 + 1 tabl
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