Publications

Order by: publication date number of citations

• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains

  Ömer Mert Aksoy, Christopher Mudry, Akira Furusaki, Apoorv Tiwari

  SciPost Phys. 16, 022 (2024) · published 22 January 2024 | Toggle abstract · pdf

  Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be local in this paper). LSM theorems have recently been interpreted as the lattice counterparts to mixed 't Hooft anomalies in quantum field theories that arise from a combination of crystalline and global internal symmetry groups. Accordingly, LSM theorems have been reinterpreted as LSM anomalies. In this work, we provide a systematic diagnostic for LSM anomalies in one spatial dimension. We show that gauging subgroups of the global internal symmetry group of a quantum lattice model obeying an LSM anomaly delivers a dual quantum lattice Hamiltonian such that its internal and crystalline symmetries mix non-trivially through a group extension. This mixing of crystalline and internal symmetries after gauging is a direct consequence of the LSM anomaly, i.e., it can be used as a diagnostic of an LSM anomaly. We exemplify this procedure for a quantum spin-1/2 chain obeying an LSM anomaly resulting from combining a global internal $\mathbb{Z}^{\,}_{2}×\mathbb{Z}^{\,}_{2}$ symmetry with translation or reflection symmetry. We establish a triality of models by gauging a $\mathbb{Z}^{\,}_{2}\subset\mathbb{Z}^{\,}_{2}×\mathbb{Z}^{\,}_{2}$ symmetry in two ways, one of which amounts to performing a Kramers-Wannier duality, while the other implements a Jordan-Wigner duality. We discuss the mapping of the phase diagram of the quantum spin-1/2 $XYZ$ chains under such a triality. We show that the deconfined quantum critical transitions between Neel and dimer orders are mapped to either topological or conventional Landau-Ginzburg transitions. Finally, we extend our results to $\mathbb{Z}^{\,}_{n}$ clock models with $\mathbb{Z}^{\,}_{n}×\mathbb{Z}^{\,}_{n}$ global internal symmetry, and provide a reinterpretation of the dual internal symmetries in terms of $\mathbb{Z}^{\,}_{n}$ charge and dipole symmetries.

  1 citation

• Renormalization group and effective potential: a simple non-perturbative approach

  Jose Gaite

  SciPost Phys. Core 5, 044 (2022) · published 26 September 2022 | Toggle abstract · pdf

  We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory ($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.

  1 citation

• Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential

  Nicolas Chagnet, Koenraad Schalm

  SciPost Phys. 16, 028 (2024) · published 24 January 2024 | Toggle abstract · pdf

  We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their Umklapped copy, level repulsion occurs. Novel mode mixings between charge, sound, and their Umklapped copies appear at finite chemical potential - both at zero and finite momentum. We provide explicit examples for an ionic lattice, i.e. a periodic external chemical potential, and verify our results with numerical computations in fluid-gravity duality.

  1 citation

• DFT2kp: Effective kp models from ab-initio data

  João Victor V. Cassiano, Augusto de Lelis Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

  SciPost Phys. Codebases 25 (2024) · published 5 February 2024 | Toggle abstract · pdf

  The $k\cdot p$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\pi= p+ p_{SOC}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $k\cdot p$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a "hands-on" example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

  1 citation

• Codebase release 0.0 for DFT2kp

  João Victor V. Cassiano, Augusto de Lelis Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

  SciPost Phys. Codebases 25-r0.0 (2024) · published 5 February 2024 | Toggle abstract · src

  The $k\cdot p$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\pi= p+ p_{SOC}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $k\cdot p$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a "hands-on" example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

  1 citation

• divERGe implements various Exact Renormalization Group examples

  Jonas B. Profe, Dante M. Kennes, Lennart Klebl

  SciPost Phys. Codebases 26 (2024) · published 8 February 2024 | Toggle abstract · pdf

  We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU$^2$FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

  1 citation

• Deconfined quantum criticality in the long-range, anisotropic Heisenberg chain

  Anton Romen, Stefan Birnkammer, Michael Knap

  SciPost Phys. Core 7, 008 (2024) · published 22 February 2024 | Toggle abstract · pdf

  Deconfined quantum criticality describes continuous phase transitions that are not captured by the Landau-Ginzburg paradigm. Here, we investigate deconfined quantum critical points in the long-range, anisotropic Heisenberg chain. With matrix product state simulations, we show that the model undergoes a continuous phase transition from a valence bond solid to an antiferromagnet. We extract the critical exponents of the transition and connect them to an effective field theory obtained from bosonization techniques. We show that beyond stabilizing the valance bond order, the long-range interactions are irrelevant and the transition is well described by a double frequency sine-Gordon model. We propose how to realize and probe deconfined quantum criticality in our model with trapped-ion quantum simulators.

  1 citation

• Unconventional superconductivity in a strongly correlated band-insulator without doping

  Anwesha Chattopadhyay, H. R. Krishnamurthy, Arti Garg

  SciPost Phys. Core 4, 009 (2021) · published 28 April 2021 | Toggle abstract · pdf

  We present a novel route for attaining unconventional superconductivity in a strongly correlated system without doping. In a simple model of a correlated band insulator at half-filling we demonstrate, based on a generalization of the projected wavefunctions method, that superconductivity emerges for a broad range of model parameters when e-e interactions and the bare band-gap are both much larger than the kinetic energy, provided the system has sufficient frustration against the magnetic order. As the interactions are tuned, the superconducting phase appears sandwiched between the correlated band insulator followed by a paramagnetic metal on one side, and a ferrimagnetic metal, antiferromagnetic half-metal, and Mott insulator phases on the other side

  1 citation

• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

  Lara C. Ortmanns, Maarten R. Wegewijs, Janine Splettstoesser

  SciPost Phys. 14, 095 (2023) · published 4 May 2023 | Toggle abstract · pdf

  We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

  1 citation

• Microwave response of type-II superconductors at weak pinning

  B. V. Pashinsky, Mikhail V. Feigel'man, Anton V. Andreev

  SciPost Phys. 14, 096 (2023) · published 4 May 2023 | Toggle abstract · pdf

  Theory of linear microwave response of thin films of type-II superconductors in the mixed state is developed taking into account random spatial fluctuations of the parameters of the system, such as the order parameter, diffusion coefficient, or film thickness. In the regime of collective pinning the microwave response of the system exhibits strong frequency dispersion, arising from nonequilibrium vortex core quasiparticles. The corresponding contribution to the ac conductivity is controlled by the inelastic relaxation time, and may exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type inelastic relaxation. Debye mechanism of microwave losses may be responsible for strong effects of electromagnetic noise upon dc conductivity in the mixed state at low temperatures.

  1 citation