A functional renormalization group approach to non-equilibrium properties of mesoscopic interacting quantum systems

We present an extension of the concepts of the functional renormalization group approach to quantum many-body problems in non-equilibrium situations. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations. We discuss the influence of finite bias voltage and temperature on the current and conductance.     

Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.     

Migdal renormalization group approach to quantum spin systems

The Migdal RG approximation is extended to quantum spin systems such as the Heisenberg and XY-models. This yields the non-existence of phase transition in the two-dimensional Heisenberg model. The phase transition of the two-dimensional XY-model is also studied.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近 期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热 力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.     

Density matrix renormalization group approach for many-body open quantum systems

The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum.     

A generation-based particle–hole density-matrix renormalization group study of interacting quantum dots

The particle–hole version of the density-matrix renormalization-group method (PH-DMRG) is utilized to calculate the ground-state energy of an interacting two-dimensional quantum dot. We show that a modification of the method, termed generation-based PH-DMRG, leads to significant improvement of the results, and discuss its feasibility for the treatment of large systems. As another application we calculate the addition spectrum.     

Similarity renormalization group for few-body systems

Internucleon interactions evolved via flow equations yield soft potentials that lead to rapid variational convergence in few-body systems.     

Nonequilibrium entropy production for open quantum systems

We consider open quantum systems weakly coupled to a heat reservoir and driven by arbitrary time-dependent parameters. We derive exact microscopic expressions for the nonequilibrium entropy production and entropy production rate, valid arbitrarily far from equilibrium. By using the two-point energy measurement statistics for system and reservoir, we further obtain a quantum generalization of the integrated fluctuation theorem put forward by Seifert [Phys. Rev. Lett. 95, 040602 (2005)].     

Constraint algebra for interacting quantum systems

We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix.     

Numerical renormalization group for continuum one-dimensional systems

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.     

Single-block renormalization group: quantum mechanical problems

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture renormalization group (PRG), makes easy and natural the extension of the DMRG to higher-dimensional lattices. To test numerically this proposal, we study several quantum mechanical models in one, two and three dimensions. In 1D the performance of the standard DMRG is much better than its PRG version, however, for 2D models the PRG is more efficient than the DMRG in a variety of circumstances. In 3D the PRG performs also quite well.     

The renormalization group and quantum edge states

The role of edge states in phenomena like the quantum Hall effect is well known, and the basic physics has a wide field-theoretic interest. In this paper we introduce a new model exhibiting quantum Hall-like features. We show how the choice of boundary conditions for a one-particle Schrödinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic field. In each case, edge states arise from a non-trivial scaling limit involving the boundary condition, and chirality of the boundary condition plays an essential role. Second quantization of these quantum mechanical systems leads to a multi-particle ground state carrying a persistent current at the edge. We show that the theory quantized with this vacuum displays an “anomaly” at the edge which is the mark of a quantized Hall conductivity in the presence of an external magnetic field. These models therefore possess characteristics which make them indistinguishable from the quantum Hall effect at macroscopic distances. We also offer interpretations for the physics of such boundary conditions which may have a bearing on the nature of the excitations in these models.     

Mean field like renormalization group for disordered systems

Mean field results for small clusters of spins are combined with renormalization group ideas to give a new approximate scheme for the study of disordered systems. Dilute, random fields and random bonds Ising systems on a d-dimensional hypercubic lattice are analyzed with this new scheme.     

Nonequilibrium functional bosonization of quantum wire networks

We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. The formalism is based on nonequilibrium version of functional bosonization. A central role in this approach is played by the Keldysh action that has a form reminiscent of the theory of full counting statistics. To proceed with evaluation of physical observables, we assume the weak-tunneling regime and develop a real-time instanton method. A detailed exposition of the formalism is supplemented by two important applications: (i) tunneling into a biased Luttinger liquid with an impurity, and (ii) quantum Hall Fabry–Pérot interferometry.     

The density matrix renormalization group for ab initio quantum chemistry

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.