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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