# Morning Session: Application Challenges

From ALPS

## Talks

- Chair: Birgitta Whaley
- Speakers
- Synge Todo
- QMC challenges
- Criticality with large correction to scaling
- Supersolid: coexistence of diagonal or off-diagonal order (done on lattice)
- Deconfined criticality
- Long-range interacting systems
- Strongly anisotropic systems
- Bond-alternating spin chains (need good order parameter)

- Go beyond memory barrier
- Can one detect berry phases with QMC?

- QMC challenges
- Tomotoshi Nishino
- Classical lattice models
- Low temperatures
- Non-Hermitian problems (TMRG): violation of variational principle
- Examples of such problems?
- TM of vertex models are non-symmetric

- Examples of such problems?
- Constraint models: constraints increase number of states kept

- Classical lattice models
- Didier Poilblanc
- Generalized QDM for frustrated magnets
- Only for Abelian particles
- How does this expansion compare to CORE?
- CORE is not exact
- CORE breaks translational symmetry

- How does one parallelize ED on distributed memory?
- ??? -> Andreas Laeuchli

- Anatoly Kuklov
- Free-space supersolidity
- Ideal supersolid or relation to defects?
- Shear-module
- How to make people take ab-initio simulations be taken seriously?
- Quantum mechanics of superfluid living on dynamical extended defects network: quantum metallurgy
- Role of He3 in superfluid and mechanical properties of solid He4
- Flow problems?

- Valentin Murg
- Guifre Vidal
- Understand entanglement scaling

- Bela Bauer
- Adrien Feiguin
- I/O constraints
- Use of symmetries
- DMRG in momentum space

- Matthias Troyer
- Band gap problem of silicon
- Gap is completely wrong in LDA
- GW approximation

- What takes a cluster for the Hubbard model may take petaflop for material

- Band gap problem of silicon
- Ian McCulloch
- 1d challenges: parallelization
- Current limitation: 10000 states (with good symmetries)
- One million: maybe easier without quantum numbers
- Most pure 1d problems are understood, except time evolution
- Master equation evolution? Dissipation?
- t-J on wide ladder - revisit with petascale?
- Non-striped states out there?
- Enforce stripelessness with translational invariance
- Stripe in correlations

- Update tensor sequentially? Independently?
- DMRG to QFT?
- QED in 2+1?
- String is 1d object

- Quantum Chemistry
- Symmetry aspects: total spin excitations

- Nanotubes
- Nuclear shell models
- Big local dimension
- Complicated Hamiltonian

- Synge Todo

## Discussion

- Which methods can scale to petaflop machines?
- DMFT can (with disorder)
- Loop algorithm can
- DiagMC could
- Worm for helium: much harder
- Lanczos can
- For QDM etc.: keep matrix in memory

- DMRG: similar to Lanczos, more sceptical
- Latency problems
- I/O problems
- Forget storing matrices on disk (2 GB/core)
- Shared memory is easier: now about 64 cores, will not get beyond that
- Heisenberg spin chain on a terascale machine?