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...
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...
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....
Quantum resources have played a crucial role in our understanding of many-body systems over the past two decades. While entanglement has been extensively studied, the role of other quantum resources—such as magic, which is essential for quantum computational advantage—remains less explored.
I will begin by reviewing stabilizer Rényi entropies as a powerful measure of magic and their utility...
Non-stabilizerness, colloquially magic state resource—has emerged as the resource that separates classically simulable quantum circuits from those offering a genuine quantum-computational advantage. Although its dynamics have been mapped in digital (gate-based) architectures, almost nothing is known about how magic resources are generated in analog quantum simulators with all-to-all couplings...
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...
Stripe order is a defining feature of the high-temperature cuprate phase diagram and has been numerically shown to be the ground state of the two-dimensional Fermi-Hubbard and t-J models in specific regimes. Upon heating, stripe and superconducting orders give way to the strange metal and pseudogap phases, whose microscopic origins remain elusive. Using advanced tensor network techniques, we...
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...
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...
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...
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 initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case,...
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...
Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise...
Lattice gauge theories (LGTs) have gained increasing attention in both condensed matter and high-energy physics in recent years and have become the centre of many quantum simulation experiments. Theoretical and experimental works have shown that LGTs exhibit rich far-from-equilibrium phenomena relevant to central questions in quantum many-body physics. In this work, we discuss the connection...
We use quantum devices from IBMQ to perform digital quantum simulations of the Schwinger model. We work with a quantum link model description of the Schwinger model in its lowest dimensional representation, and use gauge invariance, in the form of the Gauss' law, to enhance quality of data from quantum simulations. One of our goals in this project is to find out if there are advantages of...
Rydberg tweezer arrays provide a platform for realizing spin-1/2 Hamiltonians with long-range tunnelings decaying according to power-law with the distance. We numerically investigate the effects of positional disorder and dimerization on the properties of excited states in such a one-dimensional system. Our model allows for the continuous tuning of dimerization patterns and disorder strength....
In this presentation, I shall discuss how one can use Symmetric tensors to study theories with local gauge symmetries and how this can be used to study 2+1D Quantum lattice models or two and three dimensional classical gauge theories using Tensor network methods like PEPS or Tensor renormalisation group.
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor-network-based algorithm to reveal the low-energy spectrum of Ising spin-glass systems with interaction graphs relevant to present-day quantum annealers. Our deterministic...
The Mott insulator–superfluid transition in the one-dimensional Bose–Hubbard model is a paradigmatic example of a second-order quantum phase transition. While mean-field approaches capture the transition itself, they fail to describe correlated excitations in the Mott phase.
We present a perturbative tensor network ansatz based on Bogoliubov–de Gennes (BdG) equations that overcomes this...
The Heisenberg antiferromagnet on the maple leaf lattice is a recent candidate host for spin liquid phases ([1, 2, 3]) and can also be realized experimentally both in natural minerals ([4, 5]) as well as synthetic compounds ([6, 7]). Employing exact diagonalization we investigate different ground states and map out the phase diagram under variations of three symmetry-inequivalent...
Determining optimal time-dependent fields to steer quantum systems is a critical yet computationally demanding
task, often complicated by vast and complex search landscapes. This work explores the application
of tensor network methodologies to navigate these high-dimensional parameter spaces in quantum optimal
control effectively. We investigate how structured, low-rank tensor...
We propose digital quantum simulation schemes of 2+1D U(1) link quantum electrodynamics and compare the results with classical tensor network simulations for benchmarking. To verify the accuracy of our quantum simulations, we employ tensor network methods as a classical benchmark, ensuring consistency in regimes where classical computations remain tractable. Our findings demonstrate the...
We introduce a model-independent method to construct Matrix Product Operator (MPO) representations of quasiparticle creation operators acting on the interacting vacuum of (quasi-)one-dimensional quantum many-body systems. This method exploits maximally localized Wannier functions constructed from single-particle states at intermediate system sizes, which provides the building blocks for a...
We study the behavior of magic as a bipartite correlation in the quantum Ising chain across its quantum phase transition, and at finite temperature. In order to quantify the magic of partitions rigorously, we formulate a hybrid scheme that combines stochastic sampling of reduced density matrices via quantum Monte Carlo, with state-of-the-art estimators for the robustness of magic - a *bona...
Cluster expansions were recently proposed as an accurate method to compute the exponential of the Hamiltonian. Since the exponential can be represented as a Projected Entangled Pair Operator (PEPO), a temperature range can be scanned by evolving through imaginary time by multiplying PEPOs and truncating them. Various truncation schemes exist, balancing accuracy and computational efficiency. We...
Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical simulation of quantum circuits is vital not only for validating and benchmarking quantum hardware but also for gaining deeper insights into the behavior of...
Using the developed thermal tensor-network approach, we investigate the spin Seebeck effect (SSE) of the triangular-lattice quantum antiferromagnet hosting spin supersolid phase. We focus on the low-temperature scaling behaviors of the normalized spin current across the interface. Using the 1D Heisenberg chain as a benchmark system, we observe a negative spinon spin current exhibiting...
We discuss the string breaking dynamics in the presence of creation of dynamical charge pair. We consider different string configuration that belong to different sectors and their ability to escape a false vacuum. We then further analyze how they set the onset critical time and critical point and local observables and entanglement profile that signal the dynamical quantum phase transition.
The $t$-$J$ model is one of the simplest theoretical models believed to capture key aspects of high-temperature superconductivity in cuprate materials. Despite extensive study, the nature of its ground state at finite doping remains unsettled. Stripe order, characterized by intertwined charge and spin density waves, appears to compete closely with d-wave superconductivity. Previous DMRG...
Non-local interactions are the key building block to allow for a spontaneous breaking of the translational symmetry. The latter represents one of the most fundamental symmetries in physics as it reflects the formation of periodic structures of mass and electric charge. Quantum matter with such a feature falls in the class of spontaneously symmetry broken (SSB) many-body phases with broken...
We introduce a matrix product operator (MPO) encoding of the Dyson series, which is the time-evolution operator for quantum systems with time-dependent Hamiltonians. The MPO can be made accurate up to arbitrary order in the timestep, the construction can be applied to both finite and infinite systems and it can handle long-range interactions.
Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key challenge within this framework is the computational cost associated with the contraction of the two-dimensional lattice, crucial for calculating state vector...
In strongly correlated systems, the interplay between mobile dopants and the antiferromagnetic (AFM) background plays a central role in emergent phenomena such as the pseudogap and the strange metal at finite temperature. In this particular regime, we investigate the microscopic structure of correlators of the nature of two-point and beyond, in the doped $t-J$ model at the thermodynamic limit...
We investigate spectral properties of the doped $t-J$ model using advanced tensor network techniques on finite cylinders. Individual METTS snapshots reveal a tendency for holes to cluster, eventually forming stripes upon cooling down. We complement these observations by using a recently developed dynamical METTS algorithm to calculate the spectral function and discuss the partition of its form...
I will discuss different approaches for simulating the roughening transition for the interface in the ferromagnetic Ising model. These approaches start from variational PEPS wavefunctions for the bulk, which are then glued together to form an interface configuration. I will consider both the 3-D classical version and the 2-D quantum version; for the former I can compare to very accurate...
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...
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...
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...
Matrix product state (MPS) numerics are the state of the art for studying ground state properties in low-dimensional quantum many-body systems. For studying low-lying excitations, there are two complementary approaches we may use: statics, where we find the low-lying eigenstates directly, and dynamics, where we simulate the time evolution of a non-stationary state. In this talk, we shall...
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...
Entanglement in lattice gauge theories (LGTs) is a topic of significant interest, but its definition and measurement are complicated by the fundamental structure of the Hilbert space. The gauge-invariance condition makes the total Hilbert space non-factorizable into local subsystems, thus precluding the direct application of standard entanglement measures like the von Neumann or Rényi...
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means
of random tensor networks (RTNs). Such tensor networks, formed by locally contracting random tensors chosen from the unitary Haar measure, define ensembles of quantum states whose properties depend only on the
tensor network geometry and bond dimensions. Of particular interest are...
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...
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...
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...
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...
I will review how spatio-temporal tensor networks naturally arise in the computation of expectation values following quantum quenches [1], and how they encode the dynamical properties of many-body quantum systems. Particular emphasis will be given to the concept of generalized temporal entanglement [2], a quantity that captures the entanglement structure across time, provides insight into the...
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...
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...
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...
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...
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,...
