Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms

Tensor renormalization group in bosonic field theory

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.

Correlation versus commensurability effects for finite bosonic systems in one-dimensional lattices

We investigate few-boson systems in finite one-dimensional multi-well traps covering the full interaction crossover from uncorrelated to fermionized particles. Our treatment of the ground state properties is based on the numerically exact Multi-Configurational Time-Dependent Hartree method. For commensurate filling we trace the fingerprints of localisation, as the interaction strength increases, in several observables like reduced density matrices, fluctuations and momentum distribution. For filling factor larger than one we observe on-site repulsion effects in the densities and fragmentation …

泵浦玻色子系统中的Fröhlich凝聚与Bose-Einstein凝聚之比较

Fröhlich versus Bose-Einstein Condensation in Pumped Bosonic Systems

针对泵浦玻色子系统高温凝聚机制，提出开放量子系统模型，发现其运动方程与Fröhlich凝聚速率方程相似，并证明关联效应能改变玻色子占据分布，从而更好描述高温凝聚。

Dimensional versus cut-off renormalization and the nucleon-nucleon potential of the effective field theory

The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of renormalizations are performed for the sum of an attractive delta function and its derivatives. The equivalence between the two forms of regularizations can be established with the use of energy-dependent bare couplings and the explicit forms of these couplings are determined.

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be …

玻色子晶格极化子的算符值流方程方法：超越Fröhlich范式的色散重整化

Operator Valued Flow Equation Approach to the Bosonic Lattice Polaron: Dispersion Renormalization Beyond the Fröhlich Paradigm

本研究针对晶格玻色极化子基态问题，提出算符值流方程方法，发现双声子散射会显著改变色散形状，且能产生Fröhlich型模型中不存在的极化子束缚态。

Regularization versus renormalization: Why are Casimir energy differences so often finite?

One of the very first applications of the quantum field theoretic vacuum state was in the development of the notion of Casimir energy. Now field theoretic Casimir energies, considered individually, are always infinite. But differences in Casimir energies (at worst regularized, not renormalized) are quite often finite --- a fortunate circumstance which luckily made some of the early calculations, (for instance, for parallel plates and hollow spheres), tolerably tractable. We shall explore the extent to which this observation can be made systematic. For instance: What are necessary and sufficien…

Cooperative spontaneous emission via renormalization approach: Classical versus semi-classical effects

We address the many-atom emission of a dilute cloud of two-level atoms through a renormalized perturbation theory. An analytical solution for the truncated coupled-dipole equations is derived, which contains an effective spectrum associated to the initial conditions. Our solution is able to distinguish precisely classical from semi-classical predictions for large atomic ensembles. This manifests as a reduction of the cooperativity in the radiated power for higher atomic excitation, in disagreement with the fully classical prediction from linear optics. Moreover, the second-order cooperative em…

Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems

We have combined the idea of renormalization group and quantum information theory. We have shown how the entanglement or concurrence evolve as the size of the system being large, i.e. the finite size scaling is obtained. Moreover, It introduces how the renormalization group approach can be implemented to obtain the quantum information properties of a many body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one dimensional Ising model in transverse field. We have found that the derivative of con…

Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics

We provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(ω)=ω^s (with 0<s<1), focusing on the equilibrium dynamics of the three possible spin components, from very weak dissipation to the quantum critical regime. Two complementary methods, the bosonic Numerical Renormalization Group (NRG) and Majorana diagrammatics, are used to explore the physical properties in a wide range of parameters. We show that the bosonic self-energy is the crucial ingredient for the description of critical fluctuations, but that many-body vertex corrections need to be incorpo…