DMRG Preprints

The pressurized Shastry-Sutherland Mott insulator SrCu2(BO3)2 has been found to host a plaquette-singlet phase and an antiferromagnetic phase that break different symmetries spontaneously.The recent experiment showed that their transition is of a first order nature, which seems against the pursuit of exotic and deconfined degrees of freedom in this famous frustrated quantum magnet. We found a new direction in this study. By applying a magnetic field to the material, we discover that SrCu2(BO3)2 exhibits a universal and metallic T-linear specific heat behavior in a large magnetitic field range close to the pressure of zero-field first order transition between plaquette-singlet and antiferromagnetic phases. Such an unexpected gapless response from an electronically gapped Mott insulator could be attributed to magnetized Dirac spinons liberated by the combined effect of magnetic field and pressure, consistently seen from our quantum many-body thermal tensor network computation of the Shastry-Sutherland model under magnetic field. Such a robust and universal T-linear specific heat phase points out the richness of the phase diagram of the material expanded by the axes of pressure and magnetic field and is calling for new theoretical frameworks to its full explanation.

The real-time evolution of strongly interacting matter remains a frontier of fundamental physics, as classical simulations are hampered by exponential Hilbert space growth and entanglement-driven bottlenecks in tensor networks. This study reports the quantum simulation of hadron dynamics within a $(1+1)$-dimensional SU(2) lattice gauge theory using a 156-qubit IBM superconducting processor. Leveraging a hardware-efficient Loop-String-Hadron (LSH) encoding, we simulate the dynamics of the physical degrees of freedom on a $60$-site lattice in the weak-coupling regime, as a crucial step toward the continuum limit. We successfully observe the light-cone propagation of a confined meson and internal oscillations indicative of early-time hadronic breathing modes. Notably, these high-fidelity results were obtained directly from the quantum data via a differential measurement protocol, together with measurement error mitigation, demonstrating a robust pathway for large-scale simulations even on noisy hardware. To validate the results, we benchmarked the quantum algorithm and outcome from the quantum processor against state-of-the-art approximated classical algorithms using CPU -- based on tensor network methods and Pauli propagation method, respectively. Furthermore, we provide a quantitative comparison demonstrating that as the system approaches the weak-coupling or the continuum limit, the quantum processor maintains a consistent structural robustness where classical tensor networks and Pauli propagation methods encounter an onset of exponential complexity or symmetry violations as an artifact of approximation in the algorithm. These results establish a scalable pathway for simulating non-Abelian dynamics on near-term quantum hardware and mark a critical step toward achieving a practical quantum advantage in high-energy physics.

The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications, such as TT-based function multiplication for nonlinear differential equations or convolutions. However, conventional methods for computing this product typically scale as at least $\mathcal{O}(χ^4)$ with respect to the TT bond dimension (TT-rank) $χ$, creating a severe computational bottleneck in practice. By combining randomized tensor-train sketching with slice selection via interpolative decomposition, we introduce Recursive Sketched Interpolation (RSI), a ``scale product'' algorithm that computes the Hadamard product of TTs at a computational cost of $\mathcal{O}(χ^3)$. Benchmarks across various TT scenarios demonstrate that RSI offers superior scalability compared to traditional methods while maintaining comparable accuracy. We generalize RSI to compute more complex operations, including Hadamard products of multiple TTs and other element-wise nonlinear mappings, without increasing the complexity beyond $\mathcal{O}(χ^3)$.

We analyze the modification of entanglement dynamics in the Grover algorithm when the qubits are subjected to single-qubit amplitude-damping or phase-flip noise. We compare quantum trajectories with full density-matrix simulations, analyzing the dynamics of averaged trajectory entanglement (TE) and operator entanglement (OE), in the respective state representation. Although not a genuine entanglement measure, both TE and OE are connected to the efficiency of matrix product state simulations and thus of fundamental interest. As in many quantum algorithms, at the end of the Grover circuit entanglement decreases as the system converges towards the target product state. While we find that this is well captured in the OE dynamics, quantum trajectories rarely follow paths of reducing entanglement. Optimized unraveling schemes can lower TE slightly, however we show that deep in the circuit OE is generally smaller than TE. This implies that matrix product density operator (MPDO) simulations of quantum circuits can in general be more efficient than quantum trajectories. In addition, we investigate the noise-rate scaling of success probabilities for both amplitude-damping and phase-flip noise in Grover's algorithm.

Matrix-product operators (MPOs) appear throughout the study of integrable lattice models, notably as the transfer matrices. They can also be used as transformations to construct dualities between such models, both invertible (including unitary) and non-invertible (including discrete gauging). We analyse how the local Yang--Baxter integrable structures are modified under such dualities. We see that the &hcedil;eck{R}-matrix, that appears in the baxterization approach to integrability, transforms in a simple manner. We further show for a broad class of MPOs that the usual Yang--Baxter $R$-matrix satisfies a modified algebra, previously identified in the unitary case, that gives a local integrable structure underlying the commuting transfer matrices of the dual model. We illustrate these results with two case studies, analysing an invertible unitary MPO and a non-invertible MPO both applied to the canonical XXZ spin chain. The former is the cluster entangler, arising in the study of symmetry-protected topological phases, while the latter is the Kramers--Wannier duality. We show several results for MPOs with exact MPO inverses that are of independent interest.

We calculate the phase diagram of the Bose-Hubbard model on a half-filled ladder lattice including the effect of finite on-site interactions. This shows that the rung-Mott insulator (RMI) phase persists to finite interaction strength, and we calculate the RMI-superfluid phase boundary in the thermodynamic limit. We show that the phases can still be distinguished using the number and parity variances, which are observables accessible in a quantum-gas microscope. Phases analogous to the RMI were found to exist in other quasi-1D lattice structures, with the lattice connectivity modifying the phase boundaries. This shows that the the presence of these phases is the result of states with one-dimensional structures being mapped onto higher dimensional systems, driven by the reduction of hopping rates along different directions.

Many computational methods in ab initio quantum chemistry are formulated in terms of high-order tensor contractions, whose cost determines the size of system that can be studied. We introduce stochastic tensor contraction to perform such operations with greatly reduced cost, and present its application to the gold-standard quantum chemistry method, coupled cluster theory with up to perturbative triples. For total energy errors more stringent than chemical accuracy, we reduce the computational scaling to that of mean-field theory, while starting to approach the mean-field absolute cost, thereby challenging the existing cost-to-accuracy landscape. Benchmarks against state-of-the-art local correlation approximations further show that we achieve an order-of-magnitude improvement in both total computation time and error, with significantly reduced sensitivity to system dimensionality and electron delocalization. We conclude that stochastic tensor contraction is a powerful computational primitive to accelerate a wide range of quantum chemistry.

We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO($N$)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of $N$. For $N=2$ and $N=3$, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for $N \ge 4$, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO($N$) symmetry, including spin-$1/2$ and spin-$1$ two-leg ladders, that realize a direct transition between an SO($N$) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.

At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional manifold $M$ -- in the ground state of a $(d-1)+1$-dimensional gapped theory and the partition function of the low energy TQFT on $M$. In particular, the conjecture implies that for $d=3$, the ground state wavefunction can determine the modular tensor category description of the low energy TQFT. We verify our conjecture for general (2+1)-dimensional Levin-Wen string-net models.

We use large-scale density-matrix renormalization group simulations with bond dimensions up to $20\ 000$ to determine the magnetization curves of spin-1 and spin-$\tfrac{3}{2}$ pyrochlore Heisenberg antiferromagnets. Both models exhibit a robust half-magnetization plateau, and we find that the same 16-site state (quadrupled unit cell) is selected in both cases on the largest 64-site cubic cluster we consider for the plateau state. This contrasts sharply with the effective quantum dimer model prediction which favors the ``R'' state, and demonstrates the breakdown of the perturbative mechanism at the Heisenberg point. These results provide a nonperturbative characterization of field-induced phases in pyrochlore magnets and predictive guidance for spin-1 and spin-$\tfrac{3}{2}$ materials.