Tensor-network methods have opened a powerful route for the study of dynamical spectral functions in two-dimensional quantum systems. However, existing approaches within the framework of infinite projected entangled-pair states construct the required renormalization tensors solely from the ground-state environment and can suffer from severe numerical instability. We identify the origin of this instability and introduce an excitation-tailored corner-transfer-matrix renormalization-group (ET-CTMRG) method to resolve it. By incorporating excitation tensors into the renormalization procedure, the method constructs a substantially more accurate effective Hamiltonian matrix and thereby yields reliable and well-converged excitation spectra. For Heisenberg antiferromagnets, it reduces truncation errors by orders of magnitude and for the particularly complex case of the supersolid phase in the triangular-lattice XXZ magnet $\mathrm{K_2Co(SeO_3)_2}$, it achieves excellent quantitative agreement with inelastic neutron-scattering measurements. ET-CTMRG therefore provides a robust framework for investigating the dynamical properties of strongly correlated quantum systems.
Glueball spectroscopy and real-time production with quantum computing require three distinct ingredients: a correlated gauge vacuum, a controlled construction of pure-gauge excitations, and a dynamical detector. We develop a physics-informed quantum-algorithm toolbox for these tasks in a $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. We use the term \emph{glueball-like} for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. A loop-gas circuit and Hamiltonian variational ansatz prepare the gauge vacuum, Wilson-loop quantum subspace expansion constructs and characterizes low-lying excitations, and eigenvector continuation imports parameter-dependent dressing without a rapidly enlarged explicit loop basis. A Bethe--Salpeter-type transition amplitude quantifies the spatial broadening of the lightest state. For dynamics, a vacuum-dressed contractible-loop counter measures excess production of localized glueball-like structures. Although demonstrated in an Abelian model, the toolbox separates preparation, construction, compression, characterization, and dynamical detection in a form that is naturally extensible to non-Abelian lattice gauge theories.
Valley splitting sets the energy scale at which spin and valley degrees of freedom hybridize in silicon quantum-well qubits, but its sensitivity to interface structure makes it difficult to predict. Using the valleyor basis, we formulate a two-band effective-mass model for intervalley coupling in a finite quantum well and develop an analytical framework for treating non-perturbative effects of shear strain and wiggle-well potentials. For a $z$-independent coupling $V_s\tau_2$, corresponding to uniform shear strain, we construct a variational state from the exact plane-wave valleyors and a hard-wall envelope. This yields closed-form expressions for the two lowest states and their splitting, including the characteristic oscillatory $|\sin(k_{\rm min}L)|$ dependence. The variational result agrees with exact diagonalization to within $\sim1\%$ for realistic couplings, and provides a simple prescription for tuning the shear strain away from the nodes to enhance the valley splitting. We further show that finite barrier heights primarily renormalize the effective width of the quantum well while preserving the oscillatory dependence. For a wiggle-well coupling $V_w\cos(k_wz)\tau_1$, the valleyor representation reveals a crossover near the $k_w=2k_1$ resonance from wiggle-dominated splitting to orbital quantization. Remarkably, at high wiggle-well amplitudes, the empty-box energy scale predominantly dictates the near-resonant valley splitting, while the wiggle-well potential enters only as a sub-leading correction. This behavior can be viewed as asymptotic freedom for spin qubits. Away from resonance, the splitting exhibits a broadly peaked resonance with diffraction-like side-lobes as a function of detuning.
Johannes L. P. Steinschuld, H. Bluhm, S. A. Jafari· 0 citations
The geometry of quantum states is a fundamental research area with applications ranging from band theory in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are usually studied, while mixed ones are needed in general, for instance to allow for finite temperatures. The geometry of mixed states, however, is much more challenging, with important aspects yet to be explored. Here, we provide one missing piece by identifying the structure that relates distance measure and curvature for general (mixed or pure) quantum states. This structure is shown to carry the physical meaning of fluctuation-dissipation---by directly relating distance measure with fluctuations and curvature with linear response---and it turns into the corresponding well-known structure for pure states, where it is K\"ahler, and only then. We thus obtain a general, simple fluctuation-dissipation picture, which, among its consequences, implies that response functions inherently probe the mixed-state quantum geometric tensor. We end by using this picture to give geometric characterizations of generic transport behaviors.
We derive the $\mathcal{P}(\Phi)_2$ measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the $\Phi^{2p}_2$ measure is formulated in the grand-canonical ensemble with a general symmetric $p$-body interaction potential which is not required to have a factorized form. Unlike in the $\Phi^4_2$ case investigated by Fr\"ohlich--Knowles--Schlein--Sohinger in \cite{FKSS25}, in the treatment of higher-order interactions, Wick renormalization generates a full hierarchy of lower-order interactions which we organize systematically using a graphical formalism. One key ingredient of our analysis is a logarithmic stability estimate for both the nonlocal Hartree functional and the many-body Hamiltonian that is uniform in the interaction range, allowing us to use the positivity of the leading $p$-body interaction to control all lower-order terms generated by the Wick counterterms.
N. Phan, Zhi-Lin Yang, Xiang-Chan Zhu· 0 citations
This work introduces Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index, and develops an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice.
Haruyuki Kawabe, Minoru Nagai, Tsuyoshi Okubo et al.· 0 citations
The k$\cdot$p method can be applied directly to first-principles energies and momentum matrix elements, but the resulting models converge slowly with the number of bands and are inexact wherever the underlying Hamiltonian is nonlocal. We show that both limitations can be largely removed by renormalizing the eigenvalue spectra of the Hermitian momentum matrices. These spectra are gauge invariant, and are identical for symmetry-related Cartesian components, hence scaling the recurring magnitudes provides a modest set of parameters that preserves degeneracies and crystal symmetry without needing to construct a symmetry-adapted basis. We choose to renormalize the models against reference eigenvalues and band velocities on rays out of a high-symmetry point. For GaP, a 15-band model can reproduce the band structure in the near-gap reference regions within a few meV. For zincblende and wurtzite AlN, similar accuracy requires 30- or 66-band models, which in the case of zincblende is traced to the strong warping in the [110] direction. The scheme readily generalizes to rocksalt PbTe, which includes spin-orbit coupling, and has L-centered valence and conduction band extrema. Further, we demonstrate, for GaP, how compact four-band Hamiltonians can be obtained by downfolding within the same renormalization scheme. Moreover, by changing the fitting regime to encompass the entire Brillouin zone, the scheme can be used to generate full-zone models that reproduce the density of states. The practical utility is illustrated with a 59-band k.p model for GaP, which can be evaluated on meshes far denser than the reference calculation, that in turn can be used both to resolve fine features in the density of states and to compute the hole conductivity at low temperature.
K. Berland· 0 citations
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