Jose L. Lado

Research lines

My research focuses on the theoretical design of quantum materials with properties that are hard to find in natural compounds: unconventional superconductivity, symmetry-broken and topological states, unconventional magnetic order, and fractionalized excitations. The work of my group is organized in three research lines:

  1. Van der Waals quantum materials: designing and engineering exotic phenomena in two-dimensional materials and their heterostructures.
  2. Quantum many-body physics: exploring the emergence of new physics in interacting, non-Hermitian and ultra-large quantum systems.
  3. Machine learning quantum materials: developing machine learning algorithms for open problems in quantum matter, in particular learning Hamiltonians from experiments.

The three lines share methods and often the same projects: low-energy and first-principles electronic structure, tensor-network and neural-network many-body solvers, and machine learning models trained on those solvers. A large part of the work is done in collaboration with experimental groups, and the methods we develop are released as open-source software. The papers listed below are a selection of recent work from the group; the complete list is under Publications.

Van der Waals quantum materials

Theory of van der Waals quantum materials

Van der Waals heterostructures make it possible to engineer elusive quantum phenomena through materials engineering, twist engineering and proximity effects. These strategies control the strength of many-body interactions and tailor the internal quantum degrees of freedom, so that states relying on the coexistence of antagonistic electronic orders can be created on demand. We develop theoretical routes to exploit this flexibility, and we work with experimental groups to realize them.

Heavy fermions and Kondo matter

Kondo lattices can be built artificially in van der Waals heterostructures and in twisted multilayers, or found intrinsically in layered rare-earth compounds, giving two-dimensional heavy-fermion states and topological Kondo phenomena.

Van der Waals multiferroics

In a two-dimensional multiferroic the magnetic order and the electric polarization are locked to each other, so that one can be controlled through the other. We established the microscopic origin of that coupling in monolayer NiI2 and of the magneto-orbital order of monolayer VCl3, and, with experimental groups, imaged it at the atomic scale. Twisting two multiferroic layers adds moiré textures, such as skyrmion phases and moiré-driven polar order, that the aligned crystal does not have.

Twisted and moiré quantum matter

Twisting or stacking two van der Waals layers creates flat bands and long-wavelength moiré patterns. In graphene multilayers this produces correlated and magnetic states that can be tuned electrically, and in magnet/superconductor heterostructures the moiré modulates the superconducting state into a topological one.

Correlated van der Waals materials

Monolayer dichalcogenides, layered magnets and their heterostructures realize correlated phases that the parent crystal does not show: doped Mott physics, nodal superconductivity, strain-induced topological crystalline order and tunable chiral spin textures. We predict them from the electronic structure and, with experimental groups, resolve them at the atomic scale.

The electronic structure methods behind this line are implemented in pyqula, an open-source library for electronic, interacting and topological properties of tight-binding models.

Quantum many-body physics

Emergence in quantum many-body physics

Interactions in strongly correlated systems create behaviors that do not exist in conventional compounds: unconventional superconductivity, correlated topological states, and fractionalized excitations. We explore the quantum matter that emerges in systems with strong many-body interactions, quasiperiodicity, and coupling to an environment. On the methods side, we develop tensor-network algorithms both for interacting models and for single-particle problems too large for any conventional solver.

Tensor-network and quantum-circuit algorithms for quantum matter

Moiré, super-moiré and quasicrystalline materials require models with millions to billions of sites. By encoding such Hamiltonians as auxiliary many-body problems, tensor networks solve their spectral, correlated and topological properties at scales orders of magnitude beyond conventional methods. The same many-body tools lead to quantum-circuit algorithms for topological invariants.

Non-Hermitian and open quantum matter

Losses and coupling to an environment can create topological modes and criticality that have no Hermitian counterpart. We study non-Hermitian interacting models with tensor networks, and design photonic lattices with engineered losses and quasiperiodic modulation, where these phenomena are observed.

Artificial topological quantum magnets

Spin chains and lattices built atom by atom, or synthesized from molecules on surfaces, realize quantum magnets with topological many-body excitations that can be probed with scanning tunneling spectroscopy.

The tensor-network methods of this line are implemented in dmrgpy, an open-source library for quantum many-body problems with tensor networks.

Machine learning quantum materials

Machine learning quantum materials

A variety of problems in quantum materials remain out of reach of conventional methods. We develop machine learning algorithms for three of them: inferring the Hamiltonian of a material from experimentally accessible measurements, reconstructing many-body correlations and entanglement from local data, and solving interacting models with neural-network quantum states. Our aim is to bring experimental data and theoretical models together, and several of these methods have already been demonstrated on experiments.

Hamiltonian learning from experimental data

Extracting the Hamiltonian of a quantum magnet or a superconductor from spectroscopy is an inverse problem with no direct solution. We train neural networks on many-body solvers so that they infer the parameters directly from scanning tunneling spectra or impurity states.

Learning correlations, entanglement and quantum criticality

The correlation entropy and the entanglement structure of a many-body state require measuring correlators over a whole sample. Neural networks trained on synthetic data reconstruct them from a few local measurements, transfer between families of Hamiltonians, and, combined with Lee-Yang theory, locate quantum phase transitions from finite systems.

Machine learning for quantum devices and photonic lattices

The same strategy of training on theory and applying to measurements tunes quantum devices and characterizes photonic lattices, in collaboration with the groups that build them.

Van der Waals quantum materials

Theory of van der Waals quantum materials

Van der Waals heterostructures make it possible to engineer elusive quantum phenomena through materials engineering, twist engineering and proximity effects. These strategies control the strength of many-body interactions and tailor the internal quantum degrees of freedom, so that states relying on the coexistence of antagonistic electronic orders can be created on demand. We develop theoretical routes to exploit this flexibility, and we work with experimental groups to realize them.

Heavy fermions and Kondo matter

Kondo lattices can be built artificially in van der Waals heterostructures and in twisted multilayers, or found intrinsically in layered rare-earth compounds, giving two-dimensional heavy-fermion states and topological Kondo phenomena.

Van der Waals multiferroics

In a two-dimensional multiferroic the magnetic order and the electric polarization are locked to each other, so that one can be controlled through the other. We established the microscopic origin of that coupling in monolayer NiI2 and of the magneto-orbital order of monolayer VCl3, and, with experimental groups, imaged it at the atomic scale. Twisting two multiferroic layers adds moiré textures, such as skyrmion phases and moiré-driven polar order, that the aligned crystal does not have.

Twisted and moiré quantum matter

Twisting or stacking two van der Waals layers creates flat bands and long-wavelength moiré patterns. In graphene multilayers this produces correlated and magnetic states that can be tuned electrically, and in magnet/superconductor heterostructures the moiré modulates the superconducting state into a topological one.

Correlated van der Waals materials

Monolayer dichalcogenides, layered magnets and their heterostructures realize correlated phases that the parent crystal does not show: doped Mott physics, nodal superconductivity, strain-induced topological crystalline order and tunable chiral spin textures. We predict them from the electronic structure and, with experimental groups, resolve them at the atomic scale.

The electronic structure methods behind this line are implemented in pyqula, an open-source library for electronic, interacting and topological properties of tight-binding models.

Quantum many-body physics

Emergence in quantum many-body physics

Interactions in strongly correlated systems create behaviors that do not exist in conventional compounds: unconventional superconductivity, correlated topological states, and fractionalized excitations. We explore the quantum matter that emerges in systems with strong many-body interactions, quasiperiodicity, and coupling to an environment. On the methods side, we develop tensor-network algorithms both for interacting models and for single-particle problems too large for any conventional solver.

Tensor-network and quantum-circuit algorithms for quantum matter

Moiré, super-moiré and quasicrystalline materials require models with millions to billions of sites. By encoding such Hamiltonians as auxiliary many-body problems, tensor networks solve their spectral, correlated and topological properties at scales orders of magnitude beyond conventional methods. The same many-body tools lead to quantum-circuit algorithms for topological invariants.

Non-Hermitian and open quantum matter

Losses and coupling to an environment can create topological modes and criticality that have no Hermitian counterpart. We study non-Hermitian interacting models with tensor networks, and design photonic lattices with engineered losses and quasiperiodic modulation, where these phenomena are observed.

Artificial topological quantum magnets

Spin chains and lattices built atom by atom, or synthesized from molecules on surfaces, realize quantum magnets with topological many-body excitations that can be probed with scanning tunneling spectroscopy.

The tensor-network methods of this line are implemented in dmrgpy, an open-source library for quantum many-body problems with tensor networks.

Machine learning quantum materials

Machine learning quantum materials

A variety of problems in quantum materials remain out of reach of conventional methods. We develop machine learning algorithms for three of them: inferring the Hamiltonian of a material from experimentally accessible measurements, reconstructing many-body correlations and entanglement from local data, and solving interacting models with neural-network quantum states. Our aim is to bring experimental data and theoretical models together, and several of these methods have already been demonstrated on experiments.

Hamiltonian learning from experimental data

Extracting the Hamiltonian of a quantum magnet or a superconductor from spectroscopy is an inverse problem with no direct solution. We train neural networks on many-body solvers so that they infer the parameters directly from scanning tunneling spectra or impurity states.

Learning correlations, entanglement and quantum criticality

The correlation entropy and the entanglement structure of a many-body state require measuring correlators over a whole sample. Neural networks trained on synthetic data reconstruct them from a few local measurements, transfer between families of Hamiltonians, and, combined with Lee-Yang theory, locate quantum phase transitions from finite systems.

Machine learning for quantum devices and photonic lattices

The same strategy of training on theory and applying to measurements tunes quantum devices and characterizes photonic lattices, in collaboration with the groups that build them.