Scientific Series

We study the low-energy effective action for relativistic superfluids obtained by integrating out the heavy fields of a UV theory. A careful renormalization procedure is required if one is interested in deriving the EFT to all orders in the light fields (at a fixed order of derivatives per field). The result suggests a general relation between finite density and spontaneous symmetry breaking for QFTs of interacting scalars with an internal global symmetry. The ground state at finite chemical potential of these systems is usually associated with a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that this expectation is always realized at one loop for complex scalar fields with arbitrary UV potential in d > 2 spacetime dimensions. The physically distinct phenomena of finite charge density and spontaneous symmetry breaking occur simultaneously. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ coincides with the pole mass. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3, at leading order in the 1/N expansion. In order to do this we compute analytically the one-loop effective potential at finite μ and zero temperature. As an application we derive in closed form the one-loop EFT for superfluid phonons for arbitrary UV scalar potentials in d > 2. From this we obtain analytically the one-loop scaling dimension of the lightest charge n operator in the $\phi^6$ conformal superfluid in d=3, at leading order in 1/n, reproducing a numerical result of Badel et al. 

Zoom Link:  https://pitp.zoom.us/j/97727675289?pwd=TWJyNzRucEhkM0JNM0NWeEdMM0xTQT09

I will describe a construction that allows to understand spinors in an arbitrary number of dimensions, with arbitrary signature. I will describe what pure spinors are, and how in low dimensions all spinors are pure. The first impure spinors arise in 8 dimensions, and "purest" impure spinors are octonions. I will describe how a spinor in an arbitrary dimension defines a set of geometric structures. The easiest example of this is how a pure spinor defines a complex structure. As one increases the dimension, the types of geometric structures that are described by spinors become more and more exotic. If time permits, I will describe some examples in 14 and 16 dimensions. Almost nothing is known about spinors in dimension beyond 16.

Zoom link:  https://pitp.zoom.us/j/94776499052?pwd=RGVURlRnaEx6REJwVE10VXhqa1Q5Zz09

Nils Siemonsen, Perimeter Institute & University of Waterloo

Dark Photon Superradiance

Gravitational and electromagnetic signatures of black hole superradiance are a unique probe of ultralight particles that are weakly-coupled to ordinary matter. Considering the lowest-order interactions one can write down for spin-1 dark photons, the kinetic mixing, a dark photon superradiance cloud sources a rotating visible electromagnetic field. A pair production cascade ensues in the superradiance cloud, resulting a turbulent plasma with strong electromagnetic emissions. The emission is expected to have a significant X-ray component and to potentially be periodic, with period set by the dark photon mass. The luminosity is comparable to the brightest X-ray sources in the Universe, allowing for searches at distances of up to hundreds of Mpc with existing telescopes. Therefore, multi-messenger search campaigns are sensitive to large parts of unexplored beyond the Standard Model parameter space.

Bruno Torres, Perimeter Institute & University of Waterloo

Optimal coupling for local entanglement extraction from a quantum field

The entanglement structure of quantum fields is of central importance in various aspects of the connection between spacetime geometry and quantum field theory. However, it is challenging to quantify entanglement between complementary regions of a quantum field theory due to the formally infinite amount of entanglement present at short distances. We present an operationally-motivated way of analyzing entanglement in a QFT by considering the entanglement which can be transferred to a set of local probes coupled to the field. In particular, using a lattice approximation to the field theory, we show how to optimize the coupling of the local probes with the field in a given region to most accurately capture the original entanglement present between that region and its complement. This coupling prescription establishes a bound on the entanglement between complementary regions that can be extracted to probes with finitely many degrees of freedom.

The advent of topological materials has brought with it unexpected new connections between physics and pure mathematics. In particular, algebraic topology has played a significant role in the classification of topological materials. In this talk, I will offer a brief look at an emerging chapter in this story in which algebraic geometry — in particular the algebraic geometry of moduli spaces associated with complex curves — is used to anticipate new forms of quantum matter arising from 2-dimensional hyperbolic lattices.  In the process, I will explain my recent joint works with each of J. Maciejko, E. Kienzle, and A. Nagy that establishes an electronic band theory for 2-dimensional hyperbolic matter.

Zoom link:  https://pitp.zoom.us/j/98074477672?pwd=bmVScWx1M09EaGx2ZXZrRit6NXF5dz09

The session is addressed to educating startups, SMEs, and researchers to acquire fundamental knowledge on IP within the quantum computing domain. This introductory session includes real-world examples to explain the patent process with a view to commercialization of quantum computing projects. Other forms of IP are also covered. The session is facilitated by Benjamin Mak and Marco Clementoni of Ridout & Maybee LLP. 

Zoom Link: TBD

A new approach for the first quantization of superstrings, called B-RNS-GSS formalism, is being constructed. It consists of quantizing embeddings of super surfaces into superspaces. As in the classical theory of super-embeddings, it has twistor-like variables. In this talk, besides motivating the need for such a formalism, I will review the work done in hep-th: 2211.06899, where the hetetoric supergravity equations of motion were derived from BRST nilpotency.

Zoom link:  https://pitp.zoom.us/j/98656433153?pwd=NjlpcUtITDAwWlgycUtUZUVsZ3QrQT09

We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with fixed (induced) boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that have the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required --- in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham's group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group, and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

Zoom link:  https://pitp.zoom.us/j/94369372201?pwd=NWNsYno3RmZIWUx0LytWZ09PVDVVQT09

Every unitary map with a factorisation of domain and codomain into subsystems has a well-defined causal structure given by the set of influence relations between its input and output subsystems. A causal decomposition of a unitary map U is, roughly, one that makes all there is to know about U in terms of causal structure evident and understandable in compositional terms. We'll argue that this is more than just about drawing more intuitive pictures for the causal structure of U -- it is about really understanding it at all. Now, it has been known for a while that decompositions in terms of ordinary circuit diagrams do not suffice to this end and that at least so called 'extended circuit diagrams', or 'routed circuit diagrams' are necessary, revealing a close connection between causal structure and algebraic structures that involve a particular interplay of direct sum and tensor product. Though whether or not these sorts of routed circuit diagrams suffice has been an open question since. I will give an introduction and overview of this business of causal decompositions of unitary maps, and share what is an on-going thriller.

Zoom link:  https://pitp.zoom.us/j/95689128162?pwd=RFNqWlVHMFV0RjRaakszSTBsWkZkUT09

The aim of the presentation is to review the beautiful geometry underlying the standard model of particle physics, as captured by the framework of "SO(10) grand unification." Some new observations related to how the Standard Model (SM) gauge group sits inside SO(10) will also be described. 

I will start by reviewing the SM fermion content, organising the description in terms of 2-component spinors, which give the cleanest picture. 

I will then explain a simple and concrete way to understand how spinors work in 2n dimensions, based on the algebra of differential forms in n dimensions.

This will be followed by an explanation of how a single generation of standard model fermions (including the right-handed neutrino) is perfectly described by a spinor in a 10 ("internal") dimensions. 

I will review how the two other most famous "unification" groups -- the SU(5) of Georgi-Glashow and the SO(6)xSO(4) of Pati-Salam -- sit inside SO(10), and how the SM symmetry group arises as the intersection of these two groups, when they are suitably aligned.

I will end by explaining the more recent observation that the choice of this alignment, and thus the choice of the SM symmetry group inside SO(10), is basically the choice of two Georgi-Glashow SU(5) such that the associated complex structures in R^{10} commute. This means that the SM gauge group arises from SO(10) once a "bihermitian" geometry in R^{10} is chosen. I will end with speculations as to what this geometric picture may be pointing to. 

Zoom link:  https://pitp.zoom.us/j/95984379422?pwd=SE1ybktzQzcreWREblhEUkZWWElMUT09

We study the behavior of errors in the quantum simulation of  spin systems with long-range multibody interactions resulting from the  Trotter-Suzuki decomposition of the time evolution operator. We  identify a regime where the Floquet operator underlying the Trotter  decomposition undergoes sharp changes even for small variations in the  simulation step size. This results in a time evolution operator that  is very different from the dynamics generated by the targeted  Hamiltonian, which leads to a proliferation of errors in the quantum  simulation. These regions of sharp change in the Floquet operator,  referred to as structural instability regions, appear typically at  intermediate Trotter step sizes and in the weakly interacting regime,  and are thus complementary to recently revealed quantum chaotic  regimes of the Trotterized evolution [L. M. Sieberer et al. npj  Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv.  5, eaau8342 (2019)]. We characterize these structural instability  regimes in p-spin models, transverse-field Ising models with  all-to-all p-body interactions, and analytically predict their  occurrence based on unitary perturbation theory. We further show that  the effective Hamiltonian associated with the Trotter decomposition of  the unitary time-evolution operator, when the Trotter step size is  chosen to be in the structural instability region, is very different  from the target Hamiltonian, which explains the large errors that can  occur in the simulation in the regions of instability. These results  have implications for the reliability of near-term gate based quantum  simulators, and reveal an important interplay between errors and the  physical properties of the system being simulated.

Zoom link:  https://pitp.zoom.us/j/92045582127?pwd=WDUxcnlIeXdnVWM3WGJoSFVMNDE2dz09

The Berry phase, discovered by M.V. Berry in 1984, has been applied to the construction of various invariants in topological phase of matters. The Berry phase measures the non-triviality of a uniquely gapped system as a family and takes its value in $H^2({parameter space};Z)$.

In recent years, there have been several attempts to generalize it to higher-dimensional many-body lattice systems[1,2,3,4], called the “higher” Berry phase. In the case of spatial dimension d it is believed that the higher Berry phase takes its value in $H^{d+2}({parameter space};Z)$. However, in general dimensions, the definition of the higher Berry phase in lattice systems is not yet known.

In my talk, I’ll explain about the way to extract the higher Berry phase in 1-dimensional systems by using the “higher inner product” of three matrix product states and how to construct the topological invariant which takes its value in $H^3({parameter space};Z)$. This talk is based on [3] and [4].

Refs:
[1] A. Kapustin and L. Spodyneiko Phys. Rev. B 101, 235130
[2] X. Wen, M. Qi, A. Beaudry, J. Moreno, M. J. Pflaum, D. Spiegel, A. Vishwanath and M. Hermele arXiv:2112.07748
[3] S. Ohyama, Y. Terashima and  K. Shiozaki arXiv:2303.04252
[4] S. Ohyama and S. Ryu arXiv:2304.05356  

Zoom link:  https://pitp.zoom.us/j/93720709850?pwd=RTliMDNMRWo2V2k1MnBKUjlRMjBqZz09