arXiv subjects

Philippe Corboz

Publications and source records attributed to Philippe Corboz.

At least 19 recordsLinked to original sources

arXiv2026

Fast two-dimensional tensor-network contraction via subspace iteration

The corner transfer matrix renormalization group (CTMRG) is one of the standard contraction methods for infinite projected entangled-pair states (iPEPS), but its computational cost is dominated by repeated truncated singular value decompositions (SVDs). We introduce subspace-iteration CTMRG (SI-CTMRG), a QR-based projector construction that replaces each large-matrix SVD with an SVD of a much smaller matrix. The resulting algorithm shifts the dominant cost from decompositions to tensor contractions, making it highly suited to GPU acceleration and yielding speedups of up to two orders of magnitude over standard CTMRG. We demonstrate the efficiency and accuracy of the method for the triangular-lattice Heisenberg antiferromagnet, reaching state-of-the-art iPEPS results on a single H100 GPU in approximately 10 hours of computation.

cond-mat.str-el↗

arXiv2026

Pinwheel-shaped bound triplet pairs in the magnetization plateaus of SrCu$_2$(BO$_3$)$_2$

The sequence of magnetization plateaus at 1/8, 2/15, 1/6, 1/4, 1/3, 2/5, and 1/2 of the saturation observed in SrCu$_2$(BO$_3$)$_2$ remained a puzzle until tensor-networks-based numerical simulations suggested that the low-magnetization plateaus are stabilized as Wigner crystals of spin-2 bound states, and not as one of the standard configurations (semiclassical up-down, or crystals of triplets). We report on $^{63,65}$Cu nuclear magnetic resonance spectra up to 41.9 T: Based on constraints deduced from the 1/3 plateau, we show that the spectra in the 1/8 and 2/15 plateaus indeed agree with the prediction for the spin-2 bound states, while being incompatible with a crystal of triplets. This adds the formation of Wigner crystals of bound states as an alternative fundamental paradigm in the theory of magnetization plateaus.

cond-mat.str-el↗

arXiv2025

Accurate computation of the energy variance and $\langle\langle \mathcal{L}^\dagger \mathcal{L} \rangle\rangle$ using iPEPS

Infinite projected entangled-pair states (iPEPS) provide a powerful tensor network ansatz for two-dimensional quantum many-body systems in the thermodynamic limit. In this paper we introduce an approach to accurately compute the energy variance of an iPEPS, enabling systematic extrapolations of the ground-state energy to the exact zero-variance limit. It is based on the contraction of a large cell of tensors using the corner transfer matrix renormalization group (CTRMG) method, to evaluate the correlator between pairs of local Hamiltonian terms. We show that the accuracy of this approach is substantially higher than that of previous methods, and we demonstrate the usefulness of variance extrapolation for the Heisenberg model, for a free fermionic model, and for the Shastry-Sutherland model. Finally, we apply the approach to compute $\langle \langle \mathcal{L}^\dagger \mathcal{L} \rangle \rangle$ for an open quantum system described by the Liouvillian $\mathcal{L}$, in order to assess the quality of the steady-state solution and to locate first-order phase transitions, using the dissipative quantum Ising model as an example.

cond-mat.str-el↗

arXiv2025

Accelerating two-dimensional tensor network optimization by preconditioning

We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of evaluating energies and gradients, and an ill-conditioned optimization landscape that slows convergence. To reduce the number of optimization steps, we introduce an efficient preconditioner derived from the leading term of the metric tensor. We benchmark our method against standard optimization techniques on the Heisenberg and Kitaev models, demonstrating substantial improvements in overall computational efficiency. Our approach is broadly applicable across various contraction schemes, unit cell sizes, and Hamiltonians, highlighting the potential of preconditioned optimization to advance tensor network algorithms for strongly correlated systems.

cond-mat.str-el↗

arXiv2025

Topological and Trivial Valence-Bond Orders in Higher-Spin Kitaev Models

We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and non-topological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

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arXiv2025

Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG

We develop a QR-based corner transfer matrix renormalization group (CTMRG) framework for contracting infinite projected entangled-pair states (iPEPS) on honeycomb lattices. Our method explicitly uses the lattice's native C3v symmetry at each site, generalizing QR-based acceleration (previously limited to square lattices) to enable efficient and stable contractions. This approach achieves order-of-magnitude speedups over conventional singular value decomposition (SVD)-based CTMRG while maintaining high numerical precision. Comprehensive benchmark calculations for the spin-1/2 Heisenberg and Kitaev models demonstrate higher computational efficiency without sacrificing accuracy. We further employ our method to study the Kitaev-Heisenberg model, where we provide numerical evidence for the universal 1/r^4 decay of the dimer-dimer correlation function within the quantum spin liquid (QSL) phase. Our work establishes a framework for extending QR-based CTMRG to other lattice geometries, opening new avenues for studying exotic quantum phases with tensor networks.

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arXiv2025

Zigzag antiferromagnets in the SU(3) Hubbard model on the square lattice

SU(N) Hubbard models exhibit a rich variety of phases, which may be realized through quantum simulation with ultracold atomic gases in optical lattices. In this work we study the Mott insulating phases of the SU(3) Hubbard model at 1/3-filling using infinite projected entangled-pair states, optimized with both imaginary time evolution and variational optimization. In the limit of strong interactions we reproduce the antiferromagnetic 3-sublattice ordered state previously identified in the SU(3) Heisenberg model. At intermediate interaction strength we find antiferromagnetic states exhibiting zigzag patterns of different lengths, in agreement with previous Hartree-Fock and constrained-path auxiliary-field quantum Monte Carlo calculations. We study the color order parameter and energy anisotropy, which are discontinuous across the phase transitions. Finally, we analyze the different energy contributions in two competing phases, identifying low-energy bonds at the corners of the zigzag that help stabilize the zigzag states.

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arXiv2025

Accelerating two-dimensional tensor network contractions using QR decompositions

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 on GPUs, where tensor contractions are substantially faster than these decompositions. Here we propose a contraction scheme for $C_{4v}$-symmetric tensor networks based on combining the corner transfer matrix renormalization group (CTMRG) with QR-decompositions which are substantially faster, especially on GPUs. Our approach achieves up to two orders of magnitude speedup compared to standard CTMRG without loss of accuracy and yields state-of-the-art results for the Heisenberg and $J_1$-$J_2$ models in less than 1 h on an H100 GPU.

cond-mat.str-el↗

arXiv2025

Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states

The Shastry-Sutherland model is an effective model of the layered material SrCu$_2$(BO$_3$)$_2$, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states (iPEPS), a two-dimensional tensor network ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range $0.785(5) \le J'/J \le 0.82(1)$.

cond-mat.str-el↗

arXiv2024

Effective dimensional reduction of complex systems based on tensor networks

The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components $n$. Mean-field approximations provide an effective reduction in complexity of the models, requiring only a number of phase space variables polynomial in system size. However, this comes at the cost of losing accuracy close to critical points in the systems dynamics and an inability to capture correlations in the system. In this work, we introduce a tunable approximation scheme for Markovian spreading models on networks based on Matrix Product States (MPS). By controlling the bond dimensions of the MPS, we can investigate the effective dimensionality needed to accurately represent the exact $2^n$ dimensional steady-state distribution. We introduce the entanglement entropy as a measure of the compressibility of the system and find that it peaks just after the phase transition on the disordered side, in line with the intuition that more complex states are at the 'edge of chaos'. We compare the accuracy of the MPS with exact methods on different types of small random networks and with Markov Chain Monte Carlo methods for a simplified version of the railway network of the Netherlands with 55 nodes. The MPS provides a systematic way to tune the accuracy of the approximation by reducing the dimensionality of the systems state vector, leading to an improvement over second-order mean-field approximations for sufficiently large bond dimensions.

cond-mat.stat-mech↗

arXiv2024

Exploiting the Hermitian symmetry in tensor network algorithms

Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods based on projected entangled-pair states (PEPS). For real-valued tensors the Hermitian symmetry defines a $\mathbb{Z}_2$ symmetry on the combined bra and ket auxiliary level of the tensors. By implementing this symmetry, a speedup of the computation time by up to a factor 4 can be achieved, while expectation values of observables and reduced density matrices remain Hermitian by construction. Benchmark results based on the corner transfer matrix renormalization group (CTMRG) and higher-order tensor renormalization group (HOTRG) are presented. We also discuss how to implement the Hermitian symmetry in the complex case, where a similar speedup can be achieved.

cond-mat.str-el↗

arXiv2024

Weakly first-order melting of the 1/3 plateau in the Shastry-Sutherland model

We investigate the thermal properties of the 1/3 plateau in the Shastry-Sutherland model with infinite projected entangled-pair states (iPEPS) by performing the imaginary time evolution of the infinite temperature density matrix. We show that both the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ broken symmetries of the ground states are restored at a unique temperature where the correlation length has a peak, and that the melting of the plateau occurs via a single weakly first-order transition. We focus on the experimentally relevant coupling constants deep into the 1/3 plateau phase at $h = 1$ and $J'/J = 0.63$, which was estimated to describe the SrCu$_2$(BO$_3$)$_2$ compound. By computing the free energy we are able to locate the transition temperature around $T_c \simeq 4.8$K well above the temperature $T=2$K, at which the 1/3 plateau was observed in experiments. The investigation is supplemented by adding a bias term to the Hamiltonian and studying the induced crossover. We further map the transition line in the field-temperature phase diagram.

cond-mat.str-el↗

arXiv2024

Spectral functions with infinite projected entangled-pair states

Infinite projected entangled-pair states (iPEPS) provide a powerful tool to study two-dimensional strongly correlated systems directly in the thermodynamic limit. In this work, we extend the iPEPS toolbox by a method to efficiently evaluate non-equal time two-point correlators, enabling the computation of spectral functions. It is based on an iPEPS ansatz of the ground state in a large unit cell, with an operator applied in the center of the cell, which is evolved in real-time using the fast-full update method. At every time step, the two-point correlators within a cell are computed based on the corner transfer matrix renormalization group method. Benchmark results for the 2D transverse field Ising model show that the main features of the dynamical structure factor can already be reproduced at relatively small bond dimensions and unit cell sizes. The results for the magnon dispersion are found to be in good agreement with previous data obtained with the iPEPS excitation ansatz.

cond-mat.str-el↗

arXiv2023

Superconducting stripes in the hole-doped three-band Hubbard model

We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale 2D tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $δ\sim0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting $d$-wave superconductivity in the doping range $0.15 \lesssim δ< 0.25$, while at smaller doping around $δ\sim 1/8$ we find a strong competition between superconducting and non-superconducting stripes, including also pair density-wave states with alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.

cond-mat.str-el↗

arXiv2023

Itinerant magnetism in the triangular lattice Hubbard model at half-doping: Application to twisted transition-metal dichalcogenides

We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled pair state calculations to investigate the ground state phase diagram of the triangular lattice Hubbard model at "half doping" relative to single occupancy, i.e. at a filling of $(1\pm \frac{1}{2})$ electrons per site. The electron-doped case has a nested Fermi surface in the non-interacting limit, and hence a weak-coupling instability towards density-wave orders whose wavevectors are determined by Fermi surface nesting conditions. We find that at moderate to strong interaction strengths other spatially-modulated orders arise, with wavevectors distinct from the nesting vectors. In particular, we identify a series closely-competing itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.

cond-mat.str-el↗

arXiv2023

Incommensurate order with translationally invariant projected entangled-pair states: Spiral states and quantum spin liquid on the anisotropic triangular lattice

Simulating strongly correlated systems with incommensurate order poses significant challenges for traditional finite-size-based approaches. Confining such a phase to a finite-size geometry can induce spurious frustration, with spin spirals in frustrated magnets being a typical example. Here, we introduce an Ansatz based on infinite projected entangled-pair states (iPEPS) which overcomes these limitations and enables the direct search for the optimal spiral in the thermodynamic limit, with a computational cost that is independent of the spiral's wavelength. Leveraging this method, we simulate the Heisenberg model on the anisotropic triangular lattice, which interpolates between the square and isotropic triangular lattice limits. Besides accurately reproducing the magnetically ordered phases with arbitrary wavelength, the simulations reveal a quantum spin liquid phase emerging between the N\'eel and spin spiral phases.

cond-mat.str-el↗

arXiv2023

Improved summations of $n$-point correlation functions of projected entangled-pair states

Numerical treatment of two dimensional strongly-correlated systems is both extremely challenging and of fundamental importance. Infinite projected entangled-pair states (PEPS), a class of tensor networks, have demonstrated cutting-edge performance for ground state calculations, working directly in the thermodynamic limit. Furthermore, in recent years the application of PEPS has been extended to also low-lying excited states, using an ansatz that targets quasiparticle states above the ground state with high accuracy. A major technical challenge for those simulations is the accurate evaluation of summations of two- and three-point correlation functions with reasonable computational cost. In this work, we show how a reformulation of $n$-point functions in the context of PEPS leads to extra contributions to the results that prove to play an important role. Benchmarks for the frustrated $J_1-J_2$ Heisenberg model illustrate the improved precision, efficiency and stability of the simulations compared to previous approaches. Leveraging automatic differentiation to generate the most tedious and error-prone parts of the computation, the straightforward implementation presented here is a step towards broader adoption of the PEPS excitation ansatz in future applications.

cond-mat.str-el↗

arXiv2023

Tensor network study of the Shastry-Sutherland model with weak interlayer coupling

The layered material SrCu$_2$(BO$_3$)$_2$ has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu$_2$(BO$_3$)$_2$ under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around $J''/J\sim0.04-0.05$ than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu$_2$(BO$_3$)$_2$ to be around $J''/J\sim0.027$ at ambient pressure.

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