Related papers: Tensor Renormalization Group for interacting quant…
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)],…
Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing to capture their scale-dependent nature. The functional…
Tensor network is an attractive approach to field theory with negative sign problem. The complex $\phi^4$ theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization (TNR)…
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…
It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…
The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical and quantum systems in thermal equilibrium. At every step of the iterative…
We derive new functional renormalisation group flows for quantum gravity, in any dimension. The key new achievement is that the equations apply for any theory of gravity whose underlying Lagrangian $\sim f(R_{\mu\nu\rho\sigma})$ is a…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a…
Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the…
We propose a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice. Key to this approach is the removal of short-ranged entanglement, similar to Vidal's entanglement renormalization…
Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group algorithm. The bond weight is controlled by a single hyperparameter, whose optimal value…
Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here…
Ab-initio calculations of real-time evolution for lattice gauge theory have very interesting potential applications but present challenging computational aspects. We show that tensor renormalization group methods developed in the context of…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…