arXiv subjects

Laurens Vanderstraeten

Publications and source records attributed to Laurens Vanderstraeten.

At least 19 recordsLinked to original sources

arXiv2026

Corner entanglement scaling with projected entangled pair states

Entanglement scaling provides a powerful probe of universal properties at quantum critical points. In two dimensions, contributions originating from a corner-shaped bipartition exhibit a universal scaling, which is determined by the underlying conformal field theory. We develop a method to extract this corner entanglement entropy from projected entangled pair states directly in the thermodynamic limit. When applied to models at a quantum critical point, we show that the corner contribution exhibits scaling with the effective correlation length, in agreement with the hypothesis of finite-entanglement scaling. Our results for the corner coefficients are consistent with other methods, demonstrating the efficiency of our method for diagnosing strongly-correlated quantum critical points in two dimensions.

cond-mat.str-el↗

arXiv2026

Anyon-Impurity Bound States in Quantum-Engineered Fractional Chern Insulators

Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.

cond-mat.mes-hall↗

arXiv2026

Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series

We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

quant-ph↗

arXiv2026

Competition between pair and single-particle superfluidity in bosonic quasi-flat bands: A Gaussian state approach

The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a ``quantum geometric kernel'', thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.

cond-mat.quant-gas↗

arXiv2026

Gauge-covariant projected entangled paired states for interacting systems in a magnetic field

The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector potential. Nonetheless, in many situations all physical observables of the ground state remain entirely translation invariant. In this work, we introduce a projected entangled-pair state (PEPS) wavefunction with a pattern of virtual flux tensors, for which all physical expectation values are translation invariant by construction, possibly within an enlarged unit cell reflecting any symmetry breaking in the target state. Moreover, we show that the usual contraction and optimization methods for translation-invariant PEPS can be used, with the magnetic flux per plaquette only entering as a continuous parameter in the tensor network contractions. Therefore, our approach provides a method for simulating an interacting many-body system in a uniform magnetic field independently of the gauge choice for the vector potential and bypassing the need to consider extended magnetic unit cells.

quant-ph↗

arXiv2026

Dynamical dimer structure factor of the triangular $S=1/2$ Heisenberg antiferromagnet

The dynamical dimer structure factor is an observable probing spin-singlet excitations of quantum magnets distinct from those commonly studied by the spin structure factor. We report the dimer response for the extended spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice using large-scale GPU-accelerated matrix-product-state simulations. We investigate the ordered phases with $120^\circ$ coplanar, collinear stripe, and tetrahedral spin order, as well as candidate quantum spin-liquid (QSL) regimes, comprising an expected gapless $U(1)$ Dirac QSL and a chiral QSL at finite spin-scalar-chirality coupling. In the ordered phases, we find low-energy modes below the onset of the two-magnon continuum illustrating avoided quasiparticle decay. Within the candidate gapless QSL, we observe absolute dispersion minima at momenta of half the Brillouin zone corners, $X\equiv K/2$, in agreement with field-theory predictions that singlet monopole excitations of the $U(1)$ Dirac spin liquid become gapless at these points. Thus, the high-resolution dynamical dimer response provides support for a $U(1)$ Dirac QSL with singlet monopole excitations.

cond-mat.str-el↗

arXiv2026

Interface roughening in the 3-D Ising model with tensor networks

Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a gapped bulk. In this work, we present the first tensor-network study of the paradigmatic interface roughening transition of the 3-D Ising model using highly asymmetric lattices that are infinite in the $(xy)$ direction and finite in $z$. By reducing the problem to an effective 2-D tensor network, we study how truncating the $z$ direction reshapes the physics of the interface. For a truncation based on open boundary conditions, we demonstrate that varying the interface width gives rise to either a $\mathbb{Z}_2$ symmetry breaking transition (for odd $L_z$) or a smooth crossover(for even $L_z$). For antiperiodic boundary conditions, we obtain an effective $\mathbb{Z}_q$ clock model description with $q=2L_z$ that exhibits an intermediate Luttinger liquid phase with an emergent $\U(1)$ symmetry.

cond-mat.str-el↗

arXiv2025

Fractional Chern insulators on cylinders: Tao-Thouless states and beyond

Topological phases in two-dimensional quantum lattice models are often studied on cylinders for revealing different topological properties and making the problem numerically tractable. This makes a proper understanding of finite-circumference effects crucial for reliably extrapolating the results to the thermodynamic limit. Using matrix product states, we investigate these effects for the Laughlin-1/2 phase in the Hofstadter-Bose-Hubbard model, which can be viewed as the lattice discretization of the bosonic quantum Hall problem in the continuum. We propose a scaling of the model's parameters with the cylinder circumference that simultaneously approaches the continuum and thermodynamic limits. We find that different scaling schemes yield distinct topological signatures: we either retrieve a spontaneous formation of charge density wave ordering reminiscent of the Tao-Thouless states, known from the continuum problem on thin cylinders, or we find uniform states with a topological degeneracy that can be identified as minimally entangled states known from studies of chiral spin liquids on cylinders. Finally, we carry out a similar analysis of the non-Abelian Moore-Read phase in the same model. Our results clarify the role of symmetries in numerical studies of topologically ordered states on cylinders and highlight the role of lattice effects.

cond-mat.str-el↗

arXiv2025

Fractional Quantum Hall Wedding Cakes

This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical potential. Focusing on cylindrical geometries, we realize regions exhibiting the Laughlin-1/2 phase and its particle-hole conjugate, and confirm their topological character via the local Středa's response and Laughlin's flux insertion protocol. Our approach offers a new pathway for experimentally and numerically charting entire phase diagrams within a single system, possibly eliminating the need for independent parameter scans.

cond-mat.quant-gas↗

arXiv2025

Spectral Functions of an Extended Antiferromagnetic $S=1/2$ Heisenberg Model on the Triangular Lattice

We study an extended spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice, which includes both nearest- and next-nearest-neighbor interactions, as well as a scalar chiral term. This model exhibits a rich phase diagram featuring several competing phases: different quantum spin liquids and various magnetically ordered states, including coplanar $120^\circ$ order, stripe order, and non-coplanar tetrahedral order. We employ large-scale matrix product state simulations optimized for GPUs to obtain high-resolution dynamical responses. Our calculations reveal the spectral features across both ordered and liquid regimes of the phase diagram, which we analyze in comparison with analytical predictions and field-theoretical approaches. We identify unique signatures of the ordered phases in the form of gapless Goldstone modes at the ordering wave vectors. Our results in the $J_1-J_2$ quantum spin-liquid regime are indicative of a $U(1)$ Dirac spin liquid. In the chiral spin-liquid phase, we find signatures of spinons as the fractional excitations of the underlying theory, manifested as the onset of a two-spinon continuum that agrees with predictions from the Kalmeyer-Laughlin ansatz for the ground-state wave function, and collective modes that can be viewed as spinon bound states. We discuss finite-size effects, their consistency with the presumptions from field-theory, and review the dynamical structure factor with regard to experimentally relevant features such as the occurrence of highly dispersive signals and the global distribution of spectral weight.

cond-mat.str-el↗

arXiv2025

Gauging the variational optimization of projected entangled-pair states

Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for capturing ground state physics of two-dimensional quantum systems. However, accurately computing and minimizing the energy expectation value remains challenging, in part because the impact of the gauge degrees of freedom that are present in the tensor network representation is poorly understood. We analyze the role of gauge transformations for the case of a U(1)-symmetric PEPS with point group symmetry, thereby reducing the gauge degrees of freedom to a single class. We show how gradient-based optimization strategies exploit the gauge freedom, causing the tensor network contraction to become increasingly inaccurate and to produce artificially low variational energies. Furthermore, we develop a gauge-fixed optimization strategy that largely suppresses this effect, resulting in a more robust optimization. Our study underscores the need for gauge-aware optimization strategies to guarantee reliability of variational PEPS in general settings.

cond-mat.str-el↗

arXiv2025

Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the constrained random phase approximation to construct an effective multi-band Hubbard model, which is subsequently solved using tensor networks. Our work focuses on one-dimensional and quasi-one-dimensional materials, for which we employ the machinery of matrix product states. We apply this framework to the conjugated polymers trans-polyacetylene and polythiophene, as well as the quasi-one-dimensional charge-transfer insulator Sr2CuO3. The predicted band gaps show quantitative agreement with state-of-the-art computational techniques and experimental measurements. Beyond band gaps, tensor networks provide access to a wide range of physically relevant properties, including spin magnetization and various excitation energies. Their flexibility supports the implementation of complex Hamiltonians with longer-range interactions, while the bond dimension enables systematic control over accuracy. Furthermore, the computational cost scales efficiently with system size, demonstrating the framework's scalability.

cond-mat.str-el↗

arXiv2025

Finite-size scaling on the torus with periodic projected entangled-pair states

An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$. The numerical accuracy is comparable to state-of-the-art tensor network methods, while giving access to much more data points, and at a lower computational cost. Combining this contraction routine with the use of automatic differentiation, we arrive at an efficient algorithm for optimizing fully translation invariant projected entangled-pair states on the torus. Our benchmarks show that this method yields finite-size energy results that are comparable to those from quantum Monte Carlo simulations. When combined with field-theoretical scaling techniques, our approach enables accurate estimates of critical properties for two-dimensional quantum lattice systems.

cond-mat.str-el↗

arXiv2025

Dynamic Realization of Majorana Zero Modes in a Particle-Conserving Ladder

We present a scheme to realize a topological superconducting system supporting Majorana zero modes, within a number-conserving framework suitable for optical-lattice experiments. Our approach builds on the engineering of pair-hopping processes on a ladder geometry, using a sequence of pulses that activate single-particle hopping in a time-periodic manner. We demonstrate that this dynamic setting is well captured by an effective Hamiltonian that preserves the parity symmetry, a key requirement for the stabilization of Majorana zero modes. The phase diagram of our system is determined using a bosonization theory, which is then validated by a numerical study of the topological bulk gap and entanglement spectrum using matrix product states. Our results indicate that Majorana zero modes can be stabilized in a large parameter space, accessible in optical-lattice experiments.

quant-ph↗

arXiv2024

Fermionic tensor network methods

We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks. The graded Hilbert spaces can be readily integrated with other internal and lattice symmetries in tensor networks, and only require minor extensions to an existing tensor network software package. We review and benchmark the fermionic versions of common algorithms for matrix product states and projected entangled-pair states.

quant-ph↗

arXiv2024

Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains

We investigate the nature of the quantum phase transition in modulated SU(N) Heisenberg spin chains. In the odd-N case, the transition separates a trivial non-degenerate phase to a doubly-degenerate gapped chiral PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the $\mathbb{Z}_2$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated SU(N) Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the SU(N)$_1$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by changing the model parameters slightly.

cond-mat.str-el↗

arXiv2024

Chiral polaron formation on the edge of topological quantum matter

Immersing a mobile impurity in a quantum many-body environment can reveal fundamental properties of the background medium, hence providing a powerful probe of quantum matter. This approach is particularly intriguing when considering media with exotic properties, such as strongly-correlated phases and topological states of matter. In this work, we study the dressing of a mobile impurity interacting with a chiral mode, as provided by the edge of topological quantum matter. The resulting ''chiral polaron'' is characterized by an asymmetric spectral function, which reflects the chirality and group velocity of the topological edge mode and the drag experienced by the mobile impurity. We first build our theoretical understanding from an effective one-dimensional chiral model, which captures the hallmark signatures of the chiral polaron. We then demonstrate how this simple picture extends to realistic models of integer and fractional Chern insulator states, by adapting tensor-network methods to polaron spectroscopy. Injecting mobile impurities on the edge of topological quantum matter is shown to be a powerful tool to probe exotic edge properties, particularly suitable for cold-atom experiments.

cond-mat.quant-gas↗

arXiv2024

Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

We study the response of critical Resonating Valence Bond (RVB) spin liquids to doping with longer-range singlets, and more generally of U(1)-symmetric tensor networks to non-symmetric perturbations. Using a field theory description, we find that in the RVB, doping constitutes a relevant perturbation which immediately opens up a gap, contrary to previous observations. Our analysis predicts a very large correlation length even at significant doping, which we verify using high-accuracy numerical simulations. This emphasizes the need for careful analysis, but also justifies the use of such states as a variational ansatz for critical systems. Finally, we give an example of a PEPS where non-symmetric perturbations do not open up a gap and the U(1) symmetry re-emerges.

cond-mat.str-el↗