I am a Professor of Theoretical Physics in

Instituto de Física Universidade Federal Fluminense (UFF)

What's new:

21/05/2025: Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases 

Over the past few years, I have been studying Gaussian pure fermionic states and Gaussian mixed states, with the goal of expressing them in arbitrary Pauli bases. For previous work in this direction see here. Our recent work has now yielded a complete understanding of the pure Gaussian case (details available here). We present two key theorems: the first provides an exact Pfaffian formula for pure states in any Pauli basis, while the second establishes a recursion relation. These results have potential applications in various areas, including the computation of formation probabilities, Shannon-Rényi entropies, geometric entanglement, time evolution and dynamical phase transitions in free fermion systems, as well as post-measurement entanglement entropy. Currently, we are investigating some of these applications. More to come!

18/11/2024: Subsystem Evolution Speed as Indicator of Relaxation

For dynamical quantum matter many key features and properties address their steady states, such as the fundamental question of thermalization. However, it is a  challenge to determine practically if a system has already relaxed and reached a steady state, as this requires a priori understanding of steady-state properties, which must, in principle, be verified across a large set of observables individually. In our recent work with Jiaju, Reyhaneh and Markus, we introduced a general method to quantify the relaxation of a quantum state by measuring the speed of subsystem evolution. This approach allows us to assess the relaxation of all conceivable observables, providing a general measure of relaxation without requiring any a priori knowledge. For more details, please refer to the paper linked  Here.

14/08/2024: Measuring central charge on a universal quantum processor

In 1+1 dimensional systems, both quantum and classical, critical phenomena are typically governed by conformal symmetry. The central charge is a key quantity associated with this symmetry, defining the universality class and explicitly appearing in the Virasoro algebra. Despite its significance in 1+1D conformal field theories, the central charge has never been measured experimentally—until now. It plays a crucial role in various contexts, including the two-point correlation function of the energy-momentum tensor, the scaling of entanglement entropy, and the scaling of Shannon/Rényi entropy in quantum chains. Using IBM's quantum computer, we have successfully estimated the Shannon/Rényi entropy of the XXZ and transverse field Ising chains at their critical points, enabling us to determine the central charge. To the best of my knowledge, this is the first experimental measurement of the central charge. For more details, please refer to the paper linked  Here.

21/06/2024:Update: Efficient representation of Gaussian fermionic pure states in noncomputational bases

Our paper on the Gaussian pure states in non-computational bases is now published in Physical Review A. Please see Here.

31/05/2024: Statistical physics of principal minors: Cavity approach :

Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem is to compute the sum of powers of principal minors of a matrix which is relevant to the study of critical behaviors in quantum fermionic systems and finding a subset of maximally informative training data for a learning algorithm. Specifically, in a recent paper (see Here) with Abolfazl we took principal minors of positive square matrices as statistical weights of a random point process on the set of the matrix indices. The probability of each subset of the indices is in general proportional to a positive power of the determinant of the associated sub-matrix. We used Gaussian representation of the determinants for symmetric and positive matrices to estimate the partition function (or free energy) and the entropy of principal minors within the Bethe approximation. The results are expected to be asymptotically exact for diagonally dominant matrices with locally tree-like structures. We consider the Laplacian matrix of random regular graphs of various degree and exactly characterized the structure of the relevant minors in a mean-field model of such matrices. No (finite-temperature) phase transition is observed in this class of diagonally dominant matrices by increasing the positive power of the principal minors, which here plays the role of an inverse temperature. For further details see Here. Stay tuned for further developments in this evolving field of SPPM.

31/05/2024: Generalization of Balian-Brezin decomposition for exponentials with linear fermionic part:

Our paper on the Generalization of BB decomposition is now published in Journal of Physics A: Mathematical and Theoretical. Please see Here.

18/03/2024: A field theory representation of sum of powers of principal minors and physical applications

After four and a half years of intensive research, we (with Morteza and Abolfazl) have successfully completed our study on a novel approach for computing the Sum of Powers of Principal Minors (SPPM) through a unique Grassmann integral representation akin to field theory, complemented by mean field approximation techniques. Our initial drive was to accurately determine the Rényi entropy for the ground state of the transverse field Ising chain, a problem directly linked to SPPM calculations. Our methodology has enabled us to analytically calculate this quantity in a controlled manner. Throughout our journey, we discovered that the Hubbard model's partition function also constitutes an SPPM challenge, unveiling its broader applicability. This insight extends to several machine learning problems, including determinantal point processes, highlighting the versatility of our approach. We believe we are only beginning to uncover the vast potential of this area, suggesting numerous promising paths for future exploration. Stay tuned for further developments in this evolving field. Take a look at our paper here

07/03/2024: Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases

 Together with my master student Babak and collaborator Reyhaneh, we've recently uploaded a paper to arXiv where we present a formula for calculating the amplitudes of Gaussian states in non-computational bases, including the $\sigma^x$ and $\sigma^y$ bases. This formula revolves around the Pfaffian of a submatrix ( we call them pfaffinhos) derived from an antisymmetric matrix and exponentially simplifies the process of computing amplitudes. With this approach, determining the amplitude for a given bit string can now be accomplished in under 30 seconds for systems up to a size of 1000 when using Mathematica.

19/12/2023: Update: Identifying quantum many-body integrability and chaos using eigenstates trace distances :

Our paper one the trace distance distribution in Integrable and Chaotic many-body systems is now published in PRL. See HERE the published version.

26/10/2023: Bootstrapping entanglement in quantum spin chains :

Recently, we uploaded a paper to arXiv introducing an approach to compute the entanglement in quantum spin chains, termed "bootstraping". This technique bypasses the need to diagonalize the Hamiltonian to obtain eigenstates before calculating the entanglement. Instead, it focuses on determining the entanglement purely through consistency relations. Over the past two years, I've been tackling this challenge in partnership with my former PhD student, Arash, and my regular collaborator, Jiaju. Throughout this journey, we've gained insights from our numerous discussions with Marcello Dalmonte.

30/06/2023: Generalization of Balian-Brezin decomposition for exponentials with linear fermionic part:

Recently, we uploaded a paper to arXiv presenting an extension of Balian and Brezin's well-known result concerning the decomposition of fermionic exponentials. In collaboration with my current PhD student, Adel, and my former student, Arash, we expanded the scope of the decomposition to include cases where the exponential contains linear components. This type of decomposition holds significance in studying the dynamics of spin chains with boundaries, as well as expressing the ground state in a basis without parity number symmetry. Adel will be delivering a brief presentation on this topic at the ICTP-Saifer school.

23/06/2023: Minors or: How I learned to stop worrying and love the exponential:

Over the past four years, I have collaborated with Morteza Nattagh Najafi and Abolfazl Ramezanpour on various analytical methods for calculating the sum of powers of principal minors (SPPM) of matrices. My interest in this problem was sparked in 2015 when Sona Najafi and I discovered the connection between the Renyi entropy of the transverse field Ising chain and SPPM. Since then, I have learned that this problem arises in multiple fields, including the study of determinantal point processes. We have also demonstrated that the partition function of the Hubbard model can be formulated as an SPPM problem. Now, it's time to finalize the papers we have written and deliver presentations. I have already presented on this subject at Augsburg University, Trondheim University, ISSBS, a conference in Sao Carlos honoring Chico Alcaraz, and Uberlandia University. Next week, I will be giving a talk at IFT, Sao Paulo. This will likely be my final presentation before we submit our first paper to arXiv.

04/03/2023: My take on Margaret Atwood 's "The Handmaid's Tale": 

I recently read this book for a book club. Please see my opinion here  

10/02/2023: Identifying quantum many-body integrability and chaos using eigenstates trace distances :

With Reyhaneh Khasseh, Jiaju Zhang and Marcus Heyl recently we proposed a new measure to distinguish integrable models from the chaotic ones. The measure is based on the trace distance between the subsystem eigenstates of the Hamiltonian. It has some advantages compared to the level spacing distribution.  Please see our paper here