共查询到20条相似文献,搜索用时 15 毫秒
1.
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method. 相似文献
2.
We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular, the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG. 相似文献
3.
We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model. 相似文献
4.
We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model. We find that most of the previously observed finite-size corrections are due to the sample-to-sample fluctuation of the critical temperature and scaling predictions are fulfilled only by the new average. 相似文献
5.
YEFei DINGGuo-Hui. XUBo-Wei 《理论物理通讯》2003,40(2):169-170
We utilize the renormallzation group (RG) technique to analyze the Ising critical behavior in the double frequency Sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Ising critical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well. 相似文献
6.
Mei Yin 《Communications in Mathematical Physics》2011,304(1):175-186
The renormalization group (RG) approach is largely responsible for the considerable success that has been achieved in developing
a quantitative theory of phase transitions. Physical properties emerge from spectral properties of the linearization of the
RG map at a fixed point. This article considers RG for classical Ising-type lattice systems. The linearization acts on an
infinite-dimensional Banach space of interactions. At a trivial fixed point (zero interaction), the spectral properties of
the RG linearization can be worked out explicitly, without any approximation. The results are for the RG maps corresponding
to decimation and majority rule. They indicate spectrum of an unusual kind: dense point spectrum for which the adjoint operators
have no point spectrum at all, only residual spectrum. This may serve as a lesson in what one might expect in more general
situations. 相似文献
7.
We utilize the renormalization group (RG) technique to analyze the Ising critical behavior in the doublefrequency sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Isingcritical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well. 相似文献
8.
The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases. 相似文献
9.
In this paper we examine how the predictions of conformal invariance can be widely exploited to overcome the difficulties of the density-matrix renormalization group near quantum critical points. The main idea is to match the set of low-lying energy levels of the lattice Hamiltonian, as a function of the systems size, with the spectrum expected for a given conformal field theory in two dimensions. As in previous studies this procedure requires an accurate targeting of various excited states. Here we discuss how this can be achieved within the DMRG algorithm by means of the recently proposed Thick-restart Lanczos method. As a nontrivial benchmark we use an anisotropic spin-1 Hamiltonian with special attention to the transitions from the Haldane phase. Nonetheless, we think that this procedure could be generally valid in the study of quantum critical phenomena.Received: 20 May 2004, Published online: 5 November 2004PACS:
75.40.Mg Numerical simulation studies - 05.10.Cc Renormalization group methods - 75.10.Pq Spin chain models 相似文献
10.
《中国物理C(英文版)》2015,(9)
Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method(RGM). We start with the renormalization group equation(RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application,we find out that quite a few interaction vertices are separately invariant under certain transformations(generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime. 相似文献
11.
Renormalization group approach to spin glass systems 总被引:1,自引:0,他引:1
G. Parisi R. Petronzio F. Rosati 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,21(4):605-609
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented.
The procedure is non-standard in both the nature of the additional interactions and the coarse graining transformation, that
is performed on the overlap probability measure. Universality classes are thus naturally defined on a large set of models,
going from and Gaussian spin glasses to Ising and fully frustrated models, and others. The proposed analysis is tested numerically on
the Edwards-Anderson model in d = 4. Good estimates of the critical index ν and of T
c are obtained, and an RG flow diagram is sketched for the first time.
Received 17 November 2000 相似文献
12.
Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. 相似文献
13.
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ~ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erd?s-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems. 相似文献
14.
Zhiming Huang Haozhen Situ Cai Zhang 《International Journal of Theoretical Physics》2017,56(7):2178-2191
We study quantum coherence and quantum correlation for detecting quantum phase transition (QPT) by means of quantum renormalization group (QRG) in various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including XXZ model with DM interaction, Ising model with DM interaction and XY model with DM interaction. It is found that through enough QRG iterations, l 1 norm quantum coherence and one-norm geometric quantum discord can effectively characterize QPT. We also discuss the effect of DM interaction and anisotropy on quantum coherence and quantum correlation. 相似文献
15.
《Nuclear Physics B》1988,295(1):21-35
The first order phase transitions in the two-dimensional 10-state Potts model and in the two-dimensional Ising model with magnetic field are studied with Monte Carlo renormalization group methods. The deconfining phase transition of the four-dimensional U(1) lattice gauge theory is treated similarly. The results are not consistent with the standard discontinuity fixed point picture of first order phase transitions. In the U(1) case, where this possibility exists, they are not consistent with a second order phase transition either. The results show a discontinuous flow on the first order transition surface, which is a Monte Carlo renormalization group signal of singular RG transformations. 相似文献
16.
L. De Cesare A. Caramico D’Auria I. Rabuffo M. T. Mercaldo 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,73(3):327-339
The classical to quantum crossover, which occurs in
d-dimensional transverse field Ising model-like systems decreasing
the temperature to zero in the influence domain of the quantum
critical point (QCP), is described by employing an effective
Wilsonian renormalization group approach in 4 - ε dimensions.
The basic ingredient of the treatment is the static action arising
from a preliminary one-loop averaging over non-zero frequency
modes, which enter the original quantum one. The crossover scaling
functions for susceptibility and related thermodynamic quantities
are obtained to first order in ε as explicit functions of the
temperature and the applied magnetic field. In our static
framework, which can be easily extended to other quantum systems
exhibiting a critical line which terminates in a QCP, the suitable
procedure for observing this type of crossover through genuine
thermodynamic measurements is clarified consistently with
available experiments. Remarkably, our basic idea and results may
be usefully employed to explore also the dimensional crossover
which takes place in classical Ising-like systems with slab or
film geometry and, possibly, in other finite-size classical
systems. 相似文献
17.
Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes
The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t0=t is naturally understood where t0 is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation is semi-simple, i.e., diagonalizable; when A is not semi-simple and has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink–anti-kink and soliton–soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears. 相似文献
18.
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under spacetime diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three-parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way. 相似文献
19.
Exact equations are proposed to describe g-function flows in integrable boundary quantum field theories which interpolate between different conformal field theories in their ultraviolet and infrared limits, extending previous work where purely massive flows were treated. The approach is illustrated with flows between the tricritical and critical Ising models, but the method is not restricted to these cases and should be of use in unravelling general patterns of integrable boundary flows between pairs of conformal field theories. 相似文献
20.
H. Schoeller 《The European physical journal. Special topics》2009,168(1):179-266
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in
an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or
fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically
in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation
for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization
group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium
stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables
such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show
how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the
vertices. The method is based on a previously derived real-time RG
technique [1-4]
but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore,
for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary
frequency
axis [5]
which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative
quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic
way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling
case. 相似文献