Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Y63: New Theoretical Methods for Correlated ElectronsRecordings Available
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Sponsoring Units: DCMP Chair: Sathwik Bharadwaj, Purdue University Room: Hyatt Regency Hotel -Grant Park A |
Friday, March 18, 2022 8:00AM - 8:12AM |
Y63.00001: Momentum space entanglement of fermions: results and measurement protocols Michael Flynn, Anushya Chandran, Christopher Laumann, Long Hin Tang, Matteo Bellitti In recent decades, entanglement has emerged as a prominent diagnostic of a broad range of physical phenomena in many-body systems. While one typically considers entanglement in association with partitions of a many-body system in real-space, it is in fact possible to compute the entanglement of a quantum state by partitioning it in any single-particle basis. Here we take on the problem of computing the entanglement properties of translation-invariant systems of fermions in momentum space. We present perturbative calculations for both Fermi liquids and mean-field s-wave superconductors which reveal universal aspects of their Renyi entropies. We will also discuss measurement protocols that should allow for the measurement of momentum-space entanglement, including the case in which global symmetries are present. |
Friday, March 18, 2022 8:12AM - 8:24AM |
Y63.00002: Emergent channel over a pair of pockets in strong density waves Yi Zhang, Di-Zhao Zhu Different channels over which electrons scatter between parts of the Fermi surface are the key to various electronic quantum matters, such as superconductivity and density waves. We consider an effective model in higher dimensions where each of the two pockets in the original model maps to (the Landau levels of) two Dirac fermions. We discover an emergent channel when two Dirac fermions from different pairs annihilate, where the presence of a strong density wave is essential. We support our analysis with numerical calculations on model examples in the vicinity of ferromagnetic and antiferromagnetic orders. We also discuss interesting consequences on electron interaction channels that beyond-mean-field fluctuations may induce. |
Friday, March 18, 2022 8:24AM - 8:36AM |
Y63.00003: Bound States of a Polaron, Bi-polaron and multiple Polarons Yuriy Malozovsky Bi-polaron and multiple polarons have been considered using two particles and many-particles Green functions method. The single polaron Green’s function has been described in terms of the Dyson equation and has been incorporated into the Bi-polaron and multi-polarons Green functions. The polaron exact self-energy part incorporating three-point vertex function and describing the interaction of an electron with phonons (optical and /or acoustic) as shown include two terms. The first term stands for the self-consistent one–phonon contribution which, in fact, represents the Tamm-Dancoff approximation. The second term in the polaron self-energy describes the polaron bound states and can be written in terms of the effective scattering amplitude as shown. This approach allows to describe the polaron bound states similar to the two particles bound by the Coulomb potential. Bi-polaron bound states are described by the three sets: bi-polaron set, and two single polarons sets. Tri-polaron and quad-polaron have also been considered. A polaron, bi-polaron are considered due to the interaction of an electron with optical phonons in 3D and in 2D case with acoustic phonons where bound states exist even in the case of the weak electron-phonon coupling. The Bose condensation of bi-polaron and/or multi-polaron gas in a layered 2D system with interlayer coupling is discussed. |
Friday, March 18, 2022 8:36AM - 8:48AM |
Y63.00004: Operator Algebra of Local Symmetric Operators and Braided Fusion n-Category Arkya Chatterjee, Xiao-Gang Wen Symmetries are ordinarily described by groups or higher groups. A symmetry selects a set of local symmetric operators which form an algebra. The algebra of all local symmetric operators determines the possible quantum phases and phase transitions, as well as all other properties allowed by the symmetry. Isomorphic algebras give rise to the same physical properties, and are regarded as equivalent symmetries. We refer to such isomorphic classes of algebra as categorical symmetries, which, by definition, describe all symmetries. We argue that an algebra of all local symmetric operators in n-dimensional space determines a non-degenerate braided fusion n-category (NBF-n-C), i.e. topological orders in one higher dimension, and isomorphic algebras give rise to the same NBF-n-C. We suggest that this NBF-n-C is a better description of symmetry than groups, since (anomalous) symmetries described by different groups can be equivalent. This description naturally includes symmetries beyond group and higher group, such as algebraic (higher) symmetries. We discuss explicit examples in the case of n=1 to make our case. |
Friday, March 18, 2022 8:48AM - 9:00AM |
Y63.00005: Green's function Zero and Symmetric Mass Generation Yichen Xu, Cenke Xu It is known that, under short-range interactions many topological superconductors (TSC) and topological insulators (TI) are trivialized, which means the boundary state of the system can be trivially gapped out by interaction without leading to symmetry breaking or topological ground state degeneracy. This phenomenon is also referred to as "symmetric mass generation" (SMG), and has attracted broad attentions from both the condensed matter and high energy physics communities. However, after the trivialization caused by interaction, some trace of the nontrivial topology of the system still persists. Previous studies have indicated that interacting topological TSC and TI could be related to the "zero" of Green's function, namely the fermion Green's function G(iω → 0) = 0. In this work, through the general "decorated defect" construction of symmetry protected topological (SPT) states, we demonstrate the existence of Green's function zero after SMG, by mapping the evaluation of the Green's function to the problem of a single particle path integral. This method can be extended to the cases without spatial translation symmetry, where the momentum space which hosts many quantized topological numbers is no longer meaningful. Using the same method one can demonstrate the existence of the Green's function zero at the "avoided topological transition" in the bulk of the system. |
Friday, March 18, 2022 9:00AM - 9:12AM |
Y63.00006: Scar states in a system of interacting chiral fermions Ivar Martin, Konstantin A Matveev We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability. |
Friday, March 18, 2022 9:12AM - 9:24AM |
Y63.00007: Matrix-product-state-based band-Lanczos solver for quantum cluster approaches Sebastian Paeckel, Thomas Koehler, Salvatore R Manmana, Benjamin Lenz In this talk we present a matrix-product-states-based band-Lanczos method as a cluster solver. We introduce and motivate different convergence criteria and discuss their impact on the stability of the results at the example of the variational cluster approximation. In order to increase the stability a continuous energy truncation is included. The capabilities of this method to calculate the self-energy functional are demonstrated for Hubbard-like models on different cluster geometries. |
Friday, March 18, 2022 9:24AM - 9:36AM Withdrawn |
Y63.00008: Calculating the self-energy of the 2d Hubbard model with Diagrammatic Monte Carlo and Algorithmic Matsubara Integration Connor Lenihan, Evgeny Kozik, James LeBlanc We have self-consistently calculated the self-energy of the 2d Hubbard model using diagrammatic Monte Carlo to evaluate the diagrammatic series to high order and Algorithmic Matsubara Integration to perform the Matsubara integrals. The symbollic integration of the Matsubara frequencies makes the real frequency dependence of the self-energy accessible with trivial analytic continuation. We use the spectral representation of the Green's functions to calculate the perturbative series with a starting point away from U=0 and so can perform calculations when U=0 is a singular point. |
Friday, March 18, 2022 9:36AM - 9:48AM |
Y63.00009: The cumulant Green's functions method for the Hubbard model Marcos Sergio Figueira S Silva, Renan N Lira, Jereson Silva-Valencia, Peter Riseborough In this work, we develop a theoretical study of the one-band Hubbard model. We introduce an alternative methodology to solve this model that might be competitive with the current methods, such as the dynamical mean-field theory [DMFT] or theoretical calculations employing different atomic clusters. We exactly diagonalize a linear atomic Hubbard cluster composed of N sites until N=9 (our computational limit). Utilizing the Lehmann representation, the atomic Green's functions are calculated and used to obtain the atomic cumulants ("seeds"). Finally, these cumulants are used as approximations to find Green's functions for the lattice. |
Friday, March 18, 2022 9:48AM - 10:00AM |
Y63.00010: Mean-Operator Theorywith Hybrid Quantum-Classical Algorithm Donggyu Kim, Pureum Noh, Hyun-Yong Lee, Eun-Gook Moon Entanglement phenomena in quantum many-body systems is uncovered by recent advances in quantum science and technology, manifested in quantum advantage and observation of fractionalized particles. The traditional standard description of many-body physics, mean-field theory (MFT), fundamentally fails because entanglement of quantum many-body states cannot be captured. Here, we propose a quantum-mechanically entangled mean-operator theory (MOT) to overcome the fundamental limitation of MFT. Introducing entangled operators, it is demonstrated that MOT naturally describes highly-entangled phenomena such as topological phases and their transitions. A systematic improvement of MFT is also achieved by implanting the hybrid quantum-classical algorithm. Most notably, competition physics between spontaneously symmetry-broken and topological phases is demonstrated. A minimal set of mean-field operators is provided to prepare a non-trivial many- body state, which may be realized in near-term quantum simulations. |
Friday, March 18, 2022 10:00AM - 10:12AM |
Y63.00011: Construction of Entangled Many-body States via the Higgs Mechanism Pureum Noh, Eun-Gook Moon We provide a guiding principle to generate entanglement of quantum many-body states by applying the Higgs mechanism to systems without gauge structures. A unitary operator associated with the Higgs mechanism is constructed, named as mean-operator, and employed to prepare an entangled many-body state out of a trivial state. We investigate symmetry-protected-topological states with two Ising symmetries. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates. |
Friday, March 18, 2022 10:12AM - 10:24AM |
Y63.00012: Translation symmetry and long-range entanglement Lei Yang, Chong Wang We show that if a quantum many-body state has certain nontrivial properties under translation symmetries, it will necessarily be long-range entangled. Several powerful statements in quantum many-body physics, including the celebrated Lieb-Schultz-Mattis theorem, can be viewed as corollaries of our result. |
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