Jan de Boer, Victor Godet, Jani Kastikainen, Esko Keski-Vakkuri
SciPost Phys. Core 4, 019 (2021) ·
published 23 June 2021
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One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.
Ritabrata Bhattacharya, Dileep P. Jatkar, Arnab Kundu
SciPost Phys. Core 4, 018 (2021) ·
published 9 June 2021
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We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h = 2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We explicitly compute fermion six-point function and extract the corresponding six-point OTOC which exhibits an exponential growth with maximal chaos. Following the program of Gross-Rosenhaus, this correlator contains information of the bulk cubic coupling, at the conformal point as well as perturbatively away from it. Unlike the conformal modes with high values of h, the h = 2 mode has contact interaction dominating over the planar in the large q limit.
Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon
SciPost Phys. Core 4, 012 (2021) ·
published 11 May 2021
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We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.
