Publications

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Catalogue of phonon modes in several cuprate high-temperature superconductors from density functional theory

Noah J. Jabusch, Pavan Dayal, Alexander F. Kemper

SciPost Phys. Core 6, 018 (2023) · published 23 March 2023 | · pdf

Cuprates are promising candidates for study in developing higher temperature superconductors. A thorough understanding of a material's phonon modes enables further investigation of its emergent properties, however, no complete reference of the phonon modes exists. Here, using density functional theory, we evaluate the phonon frequencies and atomic displacements for $\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$, in their tetragonal structures. The phonon modes for all materials agree with those expected from space group symmetry and display instabilities corresponding to known low-temperature structural phase transitions.
Efficient scheme for time-dependent thermal pure quantum state: Application to the Kitaev model with armchair edges

Hirokazu Taguchi, Akihisa Koga, Yuta Murakami

SciPost Phys. Proc. 11, 003 (2023) · published 5 June 2023 | · pdf

We consider the time-dependent thermal pure quantum state method and introduce the efficient scheme to evaluate the change in physical quantities induced by the time-dependent perturbations, which has been proposed in our previous paper [H. Taguchi et al., Phys. Rev. B 105, 125137 (2022)]. Here, we treat the Kitaev model to consider the Majorana-mediated spin transport, as an example. We demonstrate how efficient our scheme is to evaluate spin oscillations induced by the magnetic field pulse.
Quantum spin nematic liquid in the low-dimensional anisotropic magnets -S=1/2 delta spin chain with the anisotropic ferromagnetic interaction in magnetic field-

Toru Sakai, Rito Furuchi, Hiroki Nakano, Kiyomi Okamoto

SciPost Phys. Proc. 11, 001 (2023) · published 5 June 2023 | · pdf

The magnetization process of the $S=1/2$ delta chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the spin nematic liquid phase appears in higher magnetization region, as well as the SDW liquid one in lower region.
Manifold curvature and Ehrenfest forces with a moving basis

Jessica F. K. Halliday, Emilio Artacho

SciPost Phys. 12, 020 (2022) · published 13 January 2022 | · pdf

Known force terms arising in the Ehrenfest dynamics of quantum electrons and classical nuclei, due to a moving basis set for the former, can be understood in terms of the curvature of the manifold hosting the quantum states of the electronic subsystem. Namely, the velocity-dependent terms appearing in the Ehrenfest forces on the nuclei acquire a geometrical meaning in terms of the intrinsic curvature of the manifold, while Pulay terms relate to its extrinsic curvature.
Downfolding the Su-Schrieffer-Heeger model

Arne Schobert, Jan Berges, Tim Wehling, Erik van Loon

SciPost Phys. 11, 079 (2021) · published 20 October 2021 | · pdf

Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study the effect of displacements on both the total energy and the electronic structure based on a single ab initio calculation. In downfolding approaches, the electronic system is reduced to a smaller number of bands, allowing for the incorporation of additional correlation and environmental effects on these bands. However, the physical contents of this downfolded model and its potential limitations are not always obvious. Here, we study the potential-energy landscape and electronic structure of the Su-Schrieffer-Heeger (SSH) model, where all relevant quantities can be evaluated analytically. We compare the exact results at arbitrary displacement with diagrammatic perturbation theory both in the full model and in a downfolded effective single-band model, which gives an instructive insight into the properties of downfolding. An exact reconstruction of the potential-energy landscape is possible in a downfolded model, which requires a dynamical electron-biphonon interaction. The dispersion of the bands upon atomic displacement is also found correctly, where the downfolded model by construction only captures spectral weight in the target space. In the SSH model, the electron-phonon coupling mechanism involves exclusively hybridization between the low- and high-energy bands and this limits the computational efficiency gain of downfolded models.
Quantum-inspired tempering for ground state approximation using artificial neural networks

Tameem Albash, Conor Smith, Quinn Campbell, Andrew D. Baczewski

SciPost Phys. 14, 121 (2023) · published 19 May 2023 | · pdf

A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
Fluctuation based interpretable analysis scheme for quantum many-body snapshots

Henning Schlömer, Annabelle Bohrdt

SciPost Phys. 15, 099 (2023) · published 18 September 2023 | · pdf

Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning [Nat. Phys. 13, 435 (2017)] with correlation convolutional neural networks [Nat. Commun. 12, 3905 (2021)], which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations — which indirectly include contributions from higher order, long-range correlations — the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors [Phys. Rev. Lett. 62, 957 (1989)]. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.
Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

Harun Al Rashid, Dheeraj Kumar Singh

SciPost Phys. 16, 107 (2024) · published 22 April 2024 | · pdf

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature $T_N$ and a relatively higher temperature scale $T^*$, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from ($\pi/2, \pi/2$) toward $(\pi, 0)$ along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the $d$-wave state and pseudogap phase of high-$T_c$ cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near ($\pi/2, \pi/2$) whereas it is the smallest near $(\pi, 0)$. These spectral features survive beyond $T_N$. The temperature window $T_N \lesssim T \lesssim T^*$ shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.
Electron addition spectral functions of low-density polaron liquids

Alberto Nocera, Mona Berciu

SciPost Phys. 15, 110 (2023) · published 22 September 2023 | · pdf

Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, $E_F\gg \Omega$, requiring a large carrier concentration $x$) and in the single polaron limit (at $x=0$). Here we show that the region with $x\ll 1$ ($E_F <\Omega$) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as $x<0.1$ and the adiabaticity ratio $\Omega/t>0.5$. Unlike in the Migdal limit, here 'polaronic physics' emerges already at moderate couplings. The relevance of these results for a spinful low-$x$ metal is also discussed.
Pfaffian invariant identifies magnetic obstructed atomic insulators

Isidora Araya Day, Anastasiia Varentcova, Daniel Varjas, Anton R. Akhmerov

SciPost Phys. 15, 114 (2023) · published 25 September 2023 | · pdf

We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.

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