Related papers: Continuum field theory of matchgate tensor network…
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N = 1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using…
The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states…
We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to…
We argue that the natural way to generalise a tensor network variational class to a continuous quantum system is to use the Feynman path integral to implement a continuous tensor contraction. This approach is illustrated for the case of a…
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the…
We discuss a large class of classical field theories with continuous translation symmetry. In the quantum theory, a new anomaly explicitly breaks this translation symmetry to a discrete symmetry. Furthermore, this discrete translation…
We discuss the momentum-space topology of 3+1 and 2+1 strongly correlated fermionic systems. For the 3+1 systems the important universality class is determined by the topologically stable Fermi points in momentum space. In the extreme limit…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
Three mutually perpendicular symmetry axes of the second order, inversion, and time reversal can be used to construct a double point group denoted by D2h(TD). Properties of this group are analyzed in relation to the symmetry and…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…