Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the computational bottleneck typically lies in the singular value or eigenvalue decompositions involved in the renormalization step. This is particularly true...
We study a generalisation of $\phi_2^4$ with self coupling constant $g$ to two species coupled via the cross term $2\lambda\phi_1^2\phi_2^2$. The $\mathbb{Z}_2$ symmetry group of $\phi_2^4$ is now generalised to the diherdral group $D_4$, apart from $g=\lambda$ line where the symmetry is enhanced to $O(2)$. In $1 + 1\, d$, spontaneous breaking of continuous symmetries is forbidden....
We present a new method for extracting dynamical information from the ground state of relativistic 1+1-dimensional quantum field theories (QFTs) directly in the continuum and thermodynamic limit, using the framework of relativistic continuous matrix product states (RCMPS).
We reconstruct smeared spectral densities from static (Euclidean) two-point correlation functions, which are directly...
Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to quantum link gauge fields has been extensively studied, revealing a phase diagram that includes transitions from the columnar phase in the quantum dimer model to the resonating valence bond...
Tensor network methods have provided us with a powerful set of tools with which to study strongly interacting many-body systems on the lattice. Understanding the limitations of this approach is paramount for the success of both numerical algorithms and exact analytical representations of the many-body wavefunction. In recent years, several generalizations making use of different notions of the...
Discrete models of holographic dualities, typically modeled by tensor networks on hyperbolic tilings, produce quantum states with a characteristic quasiperiodic disorder not present in continuum holography. In this work, we study the behavior of XXZ spin chains with such symmetries, showing that lessons learned from previous non-interacting (matchgate) tensor networks generalize to more...
Ultracold gases of alkali metal atoms have attracted a lot of attention recently both in experiment and theory. The SU(2) symmetric bilinear-biquadratic (BLBQ) spin-1 Heisenberg Hamiltonian is able to model the behavior of such systems with $F=1$:
$$ H = \sum_i [(\vec S_i \otimes \vec S_{i+1})\cos\theta+(\vec S_i \otimes \vec S_{i+1})^2 \sin\theta]. $$ In the range $-\pi < \theta \le...
Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for two-dimensional quantum systems, but accurately computing and minimizing the energy expectation value remains challenging. A recent work [Tang et al., Phys. Rev. B 111, 035107 (2025)] showed that virtual gauge degrees of freedom can significantly affect the accuracy of tensor network contractions, raising...
In continuous quantum field theories with sharp corners, the entanglement entropy exhibits a universal contribution tied to the corner geometry. We investigate this intriguing phenomenon through the lens of discretized systems, specifically using infinite projected entangled pair states (iPEPS) on a lattice.
Our work demonstrates that the anticipated corner dependence naturally arises from...
We present a general computational framework for studying ground-state properties of quantum spin models on infinite two-dimensional lattices. Our approach combines automatic differentiation (AD)-based gradient optimization of infinite projected entangled-pair states (iPEPS) with variational uniform matrix product states (VUMPS) to efficiently contract infinite tensor networks with unit cell...
Higher-spin extensions of the Kitaev honeycomb model offer a fertile ground for exploring quantum frustration and topological order beyond the spin-1/2 paradigm. Despite intensive interest, the nature of their ground states remains elusive, particularly in the large‑spin regime where semiclassical intuition and entanglement effects intertwine. Accurate simulations in this limit are hindered by...
Using tangent-space methods and an extension of finite-entanglement scaling for dynamical correlations, we show the existence of a new class of one-dimensional quantum liquids: the quasi-Femi liquid. This state exhibits characteristics similar to either a Luttinger liquid or a Fermi liquid, depending on the energy scale at which it is examined. We analyze the ground state and dynamical...
Numerical simulations of quantum magnetism in two spatial dimensions are often constrained by the area law of entanglement entropy, which heavily limits the accessible system sizes in tensor network methods. In this work, we investigate how the choice of mapping from a two-dimensional lattice to a one-dimensional path affects the accuracy of the two-dimensional Density Matrix Renormalization...
The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an intertwined manner, where the superconducting order parameter is coupled to the electronic density. Employing density matrix renormalization group...
Graphene-based systems provide an outstanding platform for the study of emergent physical phenomena and exotic phases of matter. By envisioning certain low-dimensional structures with sublattice imbalances, topological defects or frustration, strongly correlated magnetic ground states with long spin coherence times have been predicted, with a plethora of applications in spintronics, quantum...
GHZ states are fundamental in quantum information science, playing roles in communication, nonlocality tests, and quantum error correction. In this work, we explore two complementary aspects of GHZ states relevant for both theory and implementation.
First, we address the structure of non-symmetric GHZ states, defined as unequal superpositions of computational basis states, which frequently...
We study existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) Gauss constraint (HITs). As discrete implementations of the celebrated anti de-Sitter/conformal field theory (AdS/CFT) correspondence, holographic states and codes have created methodological and conceptual bridges between the fields of quantum information, entanglement theory and quantum gravity....
We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. Whereas the usual approach starts from infinite temperature and evolves the state in imaginary time (towards lower temperature), our ansatz is constructed from the zero-temperature limit, the ground state, which can be found with a standard tensor network...
Real-time simulations of scattering are a promising avenue for exploring non-perturbative dynamical processes in strongly correlated systems. Unlike scattering experiments in particle colliders which measure the products of scattering, the simulations enable us to measure the system at any point in time. This allows us to directly probe the heart of the scattering process. This is particularly...
Shor’s algorithm is a major milestone in the race to quantum supremacy which proposes to factorize semiprimes in time polynomial to the length of the binary string representation of the number. However, its practical implementation is limited due to several constraints in modern-day quantum hardware. Moreover, studies benchmarking the Shor’s algorithm on quantum simulators are relatively few,...
Gauging global symmetries—promoting them to local symmetries—has been fundamental to advances in both particle physics and quantum many-body theory. In tensor network formalism, on-site unitary symmetries give rise to virtual symmetry defects within Matrix Product States (MPSs), represented by operator insertions along virtual bonds. We extend this framework to non-on-site symmetries...
In quantum systems with global symmetries, entanglement exhibits a refined structure across symmetry sectors, captured by the symmetry-resolved entanglement (SRE) entropy. In $U(1)$-symmetric free field theories, SRE entropies typically exhibit equipartition, remaining independent of the charge sector. In this work, we demonstrate the breakdown of equipartition in a random tensor network state...
We present a nonperturbative tensor network approach for computing excited states in superconducting quantum circuits, leveraging the DMRG-X algorithm. DMRG-X extends the density matrix renormalization group to target individual excited states, given a well-prepared trial state. We introduce a general strategy for constructing such trial states from the normal modes of the linearized system,...
The Bose-Hofstadter model, describing mobile bosons or fermions in a magnetic field on a lattice, hosts a plethora of interesting topological ground-state phases. The magnetic field is implemented through phases in the hopping amplitudes breaking translation invariance, which makes tensor network simulations particularly challenging. First, we show what are the convenient choices of the gauge...
We extend the known tensor decompositions for discrete tensors, as: Canonical Polyadic, Tucker, Tensor Train, Tensor Chain (MPS), Hierarchical, PEPS, etc. to a general decomposition scheme called here tensor network graph decomposition. For a given connected graph $G$ with $n$ nodes and $d$ open edges, we can decompose a given $d$-order tensor ${\cal T}\in
\mathbb{R}^{n_1\times \cdots...
Numerically determining quantum phases of matter for interacting models in two dimension is still a challenging task. There are many complementary methods to address the challenges with the feasibility sensitive to physical details. Here I identify a class of problems for which infinite PEPS method have advantages. The spontaneous symmetry breaking can have classical origin which can be...
The Rydberg blockade model on the Kagome lattice has recently been realized experimentally [1] and shown numerically—via 2D DMRG [2]—to host a $\mathbb{Z}_2$ topologically ordered phase. In this work, we investigate its phase diagram using the inherently two-dimensional tensor network ansatz: Projected Entangled Pair States (PEPS). To this end, we perform state-of-the-art variational ground...
Tensor networks offer powerful tools for compressing and manipulating high-dimensional functions, but their application outside quantum many-body theory remains relatively unexplored. In this work, we introduce TT-metadynamics, a novel adaptive biasing algorithm for classical molecular dynamics that leverages tensor train (TT) decompositions to overcome the curse of dimensionality in enhanced...
We investigate the spin-1/2 Heisenberg antiferromagnet on the ruby and maple-leaf lattices, identifying a phase transition from a gapless paramagnetic or quantum spin liquid phase on the ruby lattice to a gapped counterpart on the maple-leaf lattice. This study leverages extensive infinite variational tensor network calculations to provide new insights into the competition between ordered and...
Over the last few decades, significant progress has been made in the development of variational tensor network states (TNS) used to solve quantum field theories (QFTs). This is especially true in 1+1 dimensions, where one can take the continuum limit of matrix product states (MPS) to model both non-relativistic and relativistic fields. In this work, we instead employ a discrete approach to...
